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Local rigidity of constant mean curvature hypersurfaces in space forms 空间形式中恒定平均曲率超曲面的局部刚性
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2024-10-18 DOI: 10.1016/j.jmaa.2024.128974
Yayun Chen , Tongzhu Li
{"title":"Local rigidity of constant mean curvature hypersurfaces in space forms","authors":"Yayun Chen ,&nbsp;Tongzhu Li","doi":"10.1016/j.jmaa.2024.128974","DOIUrl":"10.1016/j.jmaa.2024.128974","url":null,"abstract":"<div><div>In this paper, we study the local rigidity of constant mean curvature (CMC) hypersurfaces. Let <span><math><mi>x</mi><mo>:</mo><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>→</mo><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>c</mi><mo>)</mo><mo>,</mo><mspace></mspace><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>, be a piece of immersed constant mean curvature hypersurface in the <span><math><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-dimensional space form <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>c</mi><mo>)</mo></math></span>. We prove that if the scalar curvature <em>R</em> is constant and the number <em>g</em> of the distinct principal curvatures satisfies <span><math><mi>g</mi><mo>≤</mo><mn>3</mn></math></span>, then <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is an isoparametric hypersurface. Further, if <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is a minimal hypersurface, then <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is a totally geodesic hypersurface for <span><math><mi>c</mi><mo>≤</mo><mn>0</mn></math></span>, and <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is either a Cartan minimal hypersurface, a Clifford minimal hypersurface, or a totally geodesic hypersurface for <span><math><mi>c</mi><mo>&gt;</mo><mn>0</mn></math></span>, which solves the high dimensional version of Bryant Conjecture.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527624","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}
引用次数: 0
Characterizations of infinitesimal relative boundedness for higher order Schrödinger operators 高阶薛定谔算子的无穷小相对有界性特征
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2024-10-18 DOI: 10.1016/j.jmaa.2024.128975
Jun Cao , Mengyao Gao , Yongyang Jin , Chao Wang
{"title":"Characterizations of infinitesimal relative boundedness for higher order Schrödinger operators","authors":"Jun Cao ,&nbsp;Mengyao Gao ,&nbsp;Yongyang Jin ,&nbsp;Chao Wang","doi":"10.1016/j.jmaa.2024.128975","DOIUrl":"10.1016/j.jmaa.2024.128975","url":null,"abstract":"<div><div>Let <span><math><mi>m</mi><mo>∈</mo><mi>N</mi></math></span> and <span><math><mi>H</mi><mo>=</mo><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>m</mi><mo>/</mo><mn>2</mn></mrow></msup><mo>+</mo><mi>V</mi></math></span> be a higher order Schrödinger operators in the Euclidean space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <span><math><mi>V</mi><mo>∈</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>loc</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>. In this paper, the authors characterize the infinitesimal relative boundedness and Trudinger's subordination for <em>H</em> on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> with <span><math><mi>p</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>, via the limit behavior of the family of operators <span><math><msub><mrow><mo>{</mo><mi>V</mi><msup><mrow><mo>(</mo><msup><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mo>−</mo><mi>m</mi><mo>/</mo><mn>2</mn></mrow></msup><mo>}</mo></mrow><mrow><mi>λ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow></msub></math></span> and a generalized Kato-type class condition. The latter is weaker than the classical Kato class condition corresponding to the case <span><math><mi>p</mi><mo>=</mo><mn>1</mn></math></span>. All these characterizations are new even when <span><math><mi>H</mi><mo>=</mo><mo>−</mo><mi>Δ</mi><mo>+</mo><mi>V</mi></math></span> is a second order Schrödinger operator.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142526968","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}
引用次数: 0
Interlacing of zeros of odd period polynomials 奇周期多项式零点的交错
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2024-10-18 DOI: 10.1016/j.jmaa.2024.128976
Grace Ko , Jennifer Mackenzie , Hui Xue
{"title":"Interlacing of zeros of odd period polynomials","authors":"Grace Ko ,&nbsp;Jennifer Mackenzie ,&nbsp;Hui Xue","doi":"10.1016/j.jmaa.2024.128976","DOIUrl":"10.1016/j.jmaa.2024.128976","url":null,"abstract":"<div><div>The work of Conrey, Farmer and Imamoglu shows that all nontrivial zeros of the odd period polynomial of a Hecke eigenform of level one lie on the unit circle. We further show that nontrivial zeros of odd period polynomials of Hecke eigenforms of different weights share certain interlacing property.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142526969","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}
引用次数: 0
Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion 具有退化各向异性扩散的非局部方程的全局存在解
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2024-10-17 DOI: 10.1016/j.jmaa.2024.128971
Maria Eckardt , Anna Zhigun
{"title":"Global existence of solutions to a nonlocal equation with degenerate anisotropic diffusion","authors":"Maria Eckardt ,&nbsp;Anna Zhigun","doi":"10.1016/j.jmaa.2024.128971","DOIUrl":"10.1016/j.jmaa.2024.128971","url":null,"abstract":"<div><div>Global existence of very weak solutions to a non-local diffusion-advection-reaction equation is established under no-flux boundary conditions in higher dimensions. The equation features degenerate myopic diffusion and nonlocal adhesion and is an extension of a mass-conserving model recently derived in <span><span>[21]</span></span>. The admissible degeneracy of the diffusion tensor is characterised in terms of the upper box fractal dimension.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142526970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence results for some nonlinear elliptic systems on graphs 图上某些非线性椭圆系统的存在性结果
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2024-10-16 DOI: 10.1016/j.jmaa.2024.128973
Shoudong Man
{"title":"Existence results for some nonlinear elliptic systems on graphs","authors":"Shoudong Man","doi":"10.1016/j.jmaa.2024.128973","DOIUrl":"10.1016/j.jmaa.2024.128973","url":null,"abstract":"<div><div>In this paper, several nonlinear elliptic systems are investigated on graphs. One type of the Sobolev embedding theorem and a new version of the strong maximum principle are established. Then, by using the variational method, the existence of different types of solutions to some elliptic systems is confirmed. Such problems extend the existence results on closed Riemann surface to graphs and extend the existence results for one single equation on graphs by Grigor'yan et al. (2016) <span><span>[12]</span></span> to nonlinear elliptic systems on graphs. Such problems can also be viewed as one type of discrete version of the elliptic systems on Euclidean space and Riemannian manifold.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142526967","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}
引用次数: 0
Error estimates of effective boundary conditions for the heat equation with optimally aligned coatings 最佳排列涂层热方程有效边界条件的误差估计
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2024-10-16 DOI: 10.1016/j.jmaa.2024.128972
Lixin Meng , Zhitong Zhou
{"title":"Error estimates of effective boundary conditions for the heat equation with optimally aligned coatings","authors":"Lixin Meng ,&nbsp;Zhitong Zhou","doi":"10.1016/j.jmaa.2024.128972","DOIUrl":"10.1016/j.jmaa.2024.128972","url":null,"abstract":"<div><div>We are interested in the validity of effective boundary conditions for a heat equation on a coated body as the thickness of the coating shrinks to zero. The coating is optimally aligned in the sense that the normal vector in the coating is an eigenvector of the thermal tensor. If the heat equation satisfies Neumann boundary condition on the outer boundary of the coating, Chen et al. (Arch. Ration. Mech. Anal. 206 (2012) 911-951) derived the complete list of effective boundary conditions satisfied by the limiting model. In this paper we provide explicit error estimates between the full model and the effective model. Moreover, our error estimates are independent of time, which shows that the maximal time interval in which the effective boundary conditions remain valid are infinite. The proof is based on <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> estimates for solutions of the full model, characterization of large time behaviors for solutions of the effective model, and interaction estimates between the two models.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445607","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}
引用次数: 0
Octahedrality and Gâteaux smoothness 八面体性和伽陀平滑性
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2024-10-16 DOI: 10.1016/j.jmaa.2024.128968
Ch. Cobollo , P. Hájek
{"title":"Octahedrality and Gâteaux smoothness","authors":"Ch. Cobollo ,&nbsp;P. Hájek","doi":"10.1016/j.jmaa.2024.128968","DOIUrl":"10.1016/j.jmaa.2024.128968","url":null,"abstract":"<div><div>We prove that every Banach space admitting a Gâteaux smooth norm and containing a complemented copy of <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> has an equivalent renorming which is simultaneously Gâteaux smooth and octahedral. This is a partial solution to an open problem from the early nineties.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Remark on square roots of self-adjoint weighted composition operators on H2 关于 H2 上自联合加权合成算子平方根的备注
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2024-10-16 DOI: 10.1016/j.jmaa.2024.128970
Sungeun Jung , Yoenha Kim , Eungil Ko
{"title":"Remark on square roots of self-adjoint weighted composition operators on H2","authors":"Sungeun Jung ,&nbsp;Yoenha Kim ,&nbsp;Eungil Ko","doi":"10.1016/j.jmaa.2024.128970","DOIUrl":"10.1016/j.jmaa.2024.128970","url":null,"abstract":"<div><div>In this paper, we study square roots of self-adjoint weighted composition operators on <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. More precisely, we focus on square roots <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>f</mi><mo>,</mo><mi>φ</mi></mrow></msub></math></span> of a self-adjoint operator <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>g</mi><mo>,</mo><mi>ψ</mi></mrow></msub><mo>=</mo><msubsup><mrow><mi>W</mi></mrow><mrow><mi>f</mi><mo>,</mo><mi>φ</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> when <em>φ</em> is a linear fractional selfmap of <span><math><mi>D</mi></math></span>. We also investigate several properties of such <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>f</mi><mo>,</mo><mi>φ</mi></mrow></msub></math></span>. Finally, we show that the square roots <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>f</mi><mo>,</mo><mi>φ</mi></mrow></msub></math></span> may be other, nonself-adjoint weighted composition operators and have nontrivial invariant subspaces.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445094","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}
引用次数: 0
Relative weak compactness in infinite-dimensional Fefferman-Meyer duality 无穷维费弗曼-迈耶对偶中的相对弱紧凑性
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2024-10-16 DOI: 10.1016/j.jmaa.2024.128969
Vasily Melnikov
{"title":"Relative weak compactness in infinite-dimensional Fefferman-Meyer duality","authors":"Vasily Melnikov","doi":"10.1016/j.jmaa.2024.128969","DOIUrl":"10.1016/j.jmaa.2024.128969","url":null,"abstract":"<div><div>Let <em>E</em> be a Banach space such that <span><math><msup><mrow><mi>E</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> has the Radon-Nikodým property. The aim of this work is to connect relative weak compactness in the <em>E</em>-valued martingale Hardy space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>μ</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> to a convex compactness criterion in a weaker topology, such as the topology of uniform convergence on compacts in measure. These results represent a dynamic version of the deep result of Diestel, Ruess, and Schachermayer on relative weak compactness in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>μ</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span>. In the reflexive case, we obtain a Kadec-Pełczyński dichotomy for <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>μ</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span>-bounded sequences, which decomposes a subsequence into a relatively weakly compact part, a pointwise weakly convexly convergent part, and a null part converging to zero uniformly on compacts in measure. As a corollary, we investigate a parameterized version of the vector-valued Komlós theorem without the assumption of <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>μ</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span>-boundedness.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445605","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}
引用次数: 0
On p-height orthogonality and characterization of inner product spaces 论 p 高度正交性和内积空间的特征
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2024-10-15 DOI: 10.1016/j.jmaa.2024.128964
Somaye Heidarirad, Ruhollah Jahanipur, Mahdi Dehghani
{"title":"On p-height orthogonality and characterization of inner product spaces","authors":"Somaye Heidarirad,&nbsp;Ruhollah Jahanipur,&nbsp;Mahdi Dehghani","doi":"10.1016/j.jmaa.2024.128964","DOIUrl":"10.1016/j.jmaa.2024.128964","url":null,"abstract":"<div><div>In this paper, we introduce and study the concept of <em>p</em>-height orthogonality in real normed linear spaces. This orthogonality generalizes the well-known Singer and height orthogonalities. First, we investigate main properties of this type of orthogonality. Then, variety of examples are presented to illustrate the relationship between <em>p</em>-height orthogonality and other previously defined (e.g., isosceles, Singer, height and Birkhoff-James) orthogonalities. Also we investigate the existence properties of this new notion of orthogonality. In particular, <em>α</em>-existence property is established and some interesting bounds for the values of <em>α</em> are obtained. Moreover, some characterizations of inner product spaces are given in terms of <em>p</em>-height orthogonality and its relation with Pythagorean and Birkhoff-James orthogonalities.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445092","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}
引用次数: 0
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