Journal of Mathematical Analysis and Applications最新文献

{"title":"Killing mean curvature solitons from Riemannian submersions","authors":"Diego Artacho ,&nbsp;Marie-Amélie Lawn ,&nbsp;Miguel Ortega","doi":"10.1016/j.jmaa.2025.130088","DOIUrl":"10.1016/j.jmaa.2025.130088","url":null,"abstract":"<div><div>We present a new general construction of mean curvature flow solitons on manifolds admitting a nowhere-vanishing Killing vector field. Using Riemannian submersion techniques, we reduce the problem from a PDE to an ODE. As an application, we obtain new examples of rotators in hyperbolic space.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"556 1","pages":"Article 130088"},"PeriodicalIF":1.2,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Synchronization of velocities in pipeline flow of blended gas","authors":"Martin Gugat","doi":"10.1016/j.jmaa.2025.130078","DOIUrl":"10.1016/j.jmaa.2025.130078","url":null,"abstract":"<div><div>We consider the pipeline flow of blended gas. The flow is governed by a coupled system where for each component we have the isothermal Euler equations with an additional velocity coupling term that couples the velocities of the different components. Our motivation is hydrogen blending in natural gas pipelines, which will play a role in the transition to renewable energies. We show that with suitable boundary conditions the velocities of the gas components synchronize exponentially fast, as long as the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm of the synchronization error is outside of a certain interval where the size of the interval is determined by the order of the interaction terms. This indicates that in some cases for a mixture of <em>n</em> components it is justified to use a drift-flux model where it is assumed that all components flow with the same velocity. For the proofs we use an appropriately chosen Lyapunov function which is based upon the idea of relative energy.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"556 1","pages":"Article 130078"},"PeriodicalIF":1.2,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An extension of the spectral fractional Laplacian to non-homogeneous boundary condition on rectangular domains, with application to well-posedness for plate equation with structural damping","authors":"Julian Edward","doi":"10.1016/j.jmaa.2025.130073","DOIUrl":"10.1016/j.jmaa.2025.130073","url":null,"abstract":"<div><div>Let Δ be the Dirichlet Laplacian on a rectangular domain <span><math><mi>R</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>. We study the mapping properties of an extension of the spectral fractional Laplacian, <span><math><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>α</mi></mrow></msup></math></span>, for <span><math><mi>α</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, when applied to functions satisfying non-homogeneous boundary conditions. A symmetry formula is proven. As an application, we prove well-posedness results for the structurally damped plate equation<span><span><span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>+</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>ρ</mi><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>α</mi></mrow></msup><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>∈</mo><mi>R</mi><mo>,</mo><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></math></span></span></span> with non-homogeneous boundary conditions<span><span><span><math><mi>u</mi><msub><mrow><mo>|</mo></mrow><mrow><mo>∂</mo><mi>R</mi></mrow></msub><mo>=</mo><mi>f</mi><mo>,</mo><mspace></mspace><mi>Δ</mi><mi>u</mi><msub><mrow><mo>|</mo></mrow><mrow><mo>∂</mo><mi>R</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mo>∂</mo><mi>R</mi><mo>×</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>)</mo><mo>.</mo></math></span></span></span> Other non-homogeneous boundary conditions are also considered.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"556 1","pages":"Article 130073"},"PeriodicalIF":1.2,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"C⁎-supports and abnormalities of operator systems","authors":"Raphaël Clouâtre ,&nbsp;Colin Krisko","doi":"10.1016/j.jmaa.2025.130074","DOIUrl":"10.1016/j.jmaa.2025.130074","url":null,"abstract":"<div><div>Let <em>S</em> be a concrete operator system represented on some Hilbert space <em>H</em>. A <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-support of <em>S</em> is the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra generated (via the Choi–Effros product) by <em>S</em> inside an injective operator system acting on <em>H</em>. By leveraging Hamana's theory, we show that such a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-support is unique precisely when <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>S</mi><mo>)</mo></math></span> (the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra generated in <span><math><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> with the usual product) is contained in every copy of the injective envelope of <em>S</em> that acts on <em>H</em>. Further, we demonstrate how the uniqueness of certain <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-supports can be used to give new characterizations of the unique extension property for ⁎-representations, as well as the hyperrigidity of <em>S</em>. In another direction, we utilize the collection of all <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-supports of <em>S</em> to describe the subspace generated by the so-called abnormalities of <em>S</em>, thereby complementing an earlier result of Kakariadis.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"556 1","pages":"Article 130074"},"PeriodicalIF":1.2,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Layer potential method for a Robin problem in Hardy spaces","authors":"Huynh Cao Truong ,&nbsp;Le Xuan Truong ,&nbsp;Tan Duc Do ,&nbsp;Nguyen Ngoc Trong","doi":"10.1016/j.jmaa.2025.130075","DOIUrl":"10.1016/j.jmaa.2025.130075","url":null,"abstract":"<div><div>Let Ω be a bounded Lipschitz domain in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>. Within an appropriate framework, we use the layer potential method to show that the Robin problem<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><mi>div</mi><mo>(</mo><mi>A</mi><mspace></mspace><mi>∇</mi><mi>u</mi><mo>)</mo><mo>=</mo><mn>0</mn><mspace></mspace><mtext>in </mtext><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mo>(</mo><mi>A</mi><mspace></mspace><mi>∇</mi><mi>u</mi><mo>)</mo><mo>⋅</mo><mi>ν</mi><mo>(</mo><mi>Q</mi><mo>)</mo><mo>+</mo><mi>b</mi><mi>u</mi><mo>(</mo><mi>Q</mi><mo>)</mo><mo>=</mo><mi>g</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mo>∂</mo><mi>Ω</mi><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><mo>(</mo><mi>∇</mi><mi>u</mi><mo>)</mo></mrow><mrow><mo>⁎</mo></mrow></msup><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mo>∂</mo><mi>Ω</mi><mo>)</mo></mtd></mtr></mtable></mrow></math></span></span></span> is uniquely solvable for all <span><math><mn>1</mn><mo>−</mo><mi>ϵ</mi><mo>&lt;</mo><mi>p</mi><mo>≤</mo><mn>1</mn></math></span>, where <span><math><mi>ϵ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>)</mo></math></span> is a suitable constant depending on the Lipschitz character of ∂Ω and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mo>∂</mo><mi>Ω</mi><mo>)</mo></math></span> denotes the atomic Hardy space on the boundary of Ω.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 2","pages":"Article 130075"},"PeriodicalIF":1.2,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A class of spectral measures and its spectral eigenvalues","authors":"Yan-Song Fu,&nbsp;Tiantian Li","doi":"10.1016/j.jmaa.2025.130079","DOIUrl":"10.1016/j.jmaa.2025.130079","url":null,"abstract":"<div><div>In this paper we will investigate the harmonic analysis of a class of infinite convolutions <em>μ</em> on <span><math><mi>R</mi></math></span>. A necessary and sufficient condition for the Hilbert space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> has an orthonormal basis of exponential functions is given. Moreover, we give a complete characterization on the spectral eigenvalues of the spectral measure <em>μ</em>, that is, to find all real numbers <em>p</em> which corresponds to a discrete set Λ such that the sets <span><math><mo>{</mo><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>π</mi><mi>i</mi><mi>λ</mi><mi>x</mi></mrow></msup><mo>:</mo><mi>λ</mi><mo>∈</mo><mi>Λ</mi><mo>}</mo></math></span> and <span><math><mo>{</mo><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>π</mi><mi>i</mi><mi>p</mi><mi>λ</mi><mi>x</mi></mrow></msup><mo>:</mo><mi>λ</mi><mo>∈</mo><mi>Λ</mi><mo>}</mo></math></span> are both orthonormal bases for <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 2","pages":"Article 130079"},"PeriodicalIF":1.2,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Strauss exponent for some k-evolution equation in the class of Boussinesq equations","authors":"Marcello D'Abbicco,&nbsp;Antonio Lagioia","doi":"10.1016/j.jmaa.2025.130077","DOIUrl":"10.1016/j.jmaa.2025.130077","url":null,"abstract":"<div><div>In this paper, we prove the existence of global small data solutions to the evolution equation<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>+</mo><mi>A</mi><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>+</mo><mi>A</mi><mi>v</mi><mo>+</mo><msup><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>v</mi><mo>=</mo><mi>A</mi><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>,</mo></mtd><mtd><mi>t</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mi>v</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mspace></mspace><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>(</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mi>A</mi><mo>=</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>a</mi><msup><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> with <span><math><mi>a</mi><mo>(</mo><mi>ξ</mi><mo>)</mo></math></span> homogeneous of order <em>k</em>, and <span><math><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>=</mo><mo>|</mo><mi>v</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>α</mi></mrow></msup></math></span> or it is a more general power nonlinearity. We prove our result for <span><math><mi>α</mi><mo>&gt;</mo><mi>γ</mi><mo>(</mo><mi>r</mi><mo>)</mo></math></span>, where <em>γ</em> is the Strauss exponent for nonlinear equations, and r is the rank of the Hessian of <span><math><mi>a</mi><mo>(</mo><mi>ξ</mi><mo>)</mo></math></span>. We also consider the damped case, obtained adding <span><math><mo>+</mo><mi>A</mi><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> to the left-hand side of the equation. We show that the effect of the dissipation is very weak, compared to the dispersion, however, it is sufficient to lower the existence exponent to some smaller, modified, Strauss exponent.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 2","pages":"Article 130077"},"PeriodicalIF":1.2,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bifurcation analysis for a spatial memory diffusive model incorporating advection term and nonlocal maturation delay","authors":"Li Ma ,&nbsp;Dan Wei ,&nbsp;Xianhua Xie","doi":"10.1016/j.jmaa.2025.130072","DOIUrl":"10.1016/j.jmaa.2025.130072","url":null,"abstract":"<div><div>A class of memory-based reaction-diffusion population models with nonlocal terms and double delays has been investigated in this research for the first time under homogeneous Dirichlet boundary conditions. Firstly, the Lyapunov-Schmidt reduction method is employed to establish the existence of non-homogeneous steady-state solutions. Simultaneously, the uniqueness and multiplicity of these solutions are also presented. Next, the local stability of the non-homogeneous steady-state solutions and sufficient conditions for the Hopf bifurcation are derived by discussing the characteristic equation near the non-homogeneous steady-state solutions <span><math><msubsup><mrow><mi>u</mi></mrow><mrow><mi>λ</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math></span>. Considering the non-homogeneous property of its characteristic equation which incorporates double delays and a non-self-adjoint operator, we will combine a prior estimation and geometric methods and prior estimation techniques to find all potential bifurcation values. We find that the presence of double delays may drive the dynamical behavior to be more complex. In addition, we also investigate the Hopf branch based only on memory delay in the model and explore the impact of the advection parameter on the generation of the Hopf branch: under some special conditions, the first critical value <span><math><msubsup><mrow><mi>r</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>λ</mi></mrow></msubsup></math></span> for Hopf branch occurrence will increase with the advection term <em>α</em>, i.e., the advective term will decelerate the presence of Hopf bifurcation to some extent. Interestingly, this phenomenon is exactly opposite to the conclusion of Ma and Wei <span><span>[20]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 2","pages":"Article 130072"},"PeriodicalIF":1.2,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Transverse FT-entropy for Riemannian foliations","authors":"Dexie Lin","doi":"10.1016/j.jmaa.2025.130070","DOIUrl":"10.1016/j.jmaa.2025.130070","url":null,"abstract":"<div><div>In this paper, we introduce an entropy functional on Riemannian foliations, inspired by the work of Perelman. We relate its gradient flow to the transverse Ricci flow via the foliation preserving diffeomorphisms. We show that it is monotonic along the transverse Ricci flow. Moreover, inspired by the work of Fuquan Fang and Yuguang Zhang, we give a sufficient condition for any codimension-4 Riemannian foliation to admit the transverse Einstein metric.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"556 1","pages":"Article 130070"},"PeriodicalIF":1.2,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Complete λ-hypersurfaces with constant norm of the second fundamental form","authors":"Pengpeng Cheng,&nbsp;Tongzhu Li","doi":"10.1016/j.jmaa.2025.130071","DOIUrl":"10.1016/j.jmaa.2025.130071","url":null,"abstract":"<div><div>In this paper, we introduce a new divergence theorem on a complete proper <em>λ</em>-hypersurface. By the new divergence theorem we classify <em>λ</em>-hypersurfaces under the conditions that the squared norm of the second fundamental form <em>S</em> and the 3-order mean curvature <span><math><msub><mrow><mi>f</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> are constant. In particular, when <span><math><mi>λ</mi><mo>=</mo><mn>0</mn></math></span>, the self-shrinker (i.e., 0-hypersurface) is either a hyperplane <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> passing through the origin, a cylinder <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>(</mo><msqrt><mrow><mi>k</mi></mrow></msqrt><mo>)</mo><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>k</mi></mrow></msup><mo>,</mo><mspace></mspace><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>n</mi><mo>−</mo><mn>1</mn></math></span>, or a round sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><msqrt><mrow><mi>n</mi></mrow></msqrt><mo>)</mo></math></span> with center at the origin.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130071"},"PeriodicalIF":1.2,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145118957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}