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The Journal of Geometric Analysis最新文献

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Logarithmic Sobolev Inequalities, Gaussian Upper Bounds for the Heat Kernel, and the $$textrm{G}_{2}$$ -Laplacian Flow 对数索波列夫不等式、热核的高斯上界以及 $$textrm{G}_{2}$ - 拉普拉卡流
The Journal of Geometric Analysis Pub Date : 2024-07-02 DOI: 10.1007/s12220-024-01697-4
Masashi Ishida
{"title":"Logarithmic Sobolev Inequalities, Gaussian Upper Bounds for the Heat Kernel, and the $$textrm{G}_{2}$$ -Laplacian Flow","authors":"Masashi Ishida","doi":"10.1007/s12220-024-01697-4","DOIUrl":"https://doi.org/10.1007/s12220-024-01697-4","url":null,"abstract":"<p>We prove a logarithmic Sobolev inequality along the <span>(textrm{G}_{2})</span>-Laplacian flow. A uniform Sololev inequality along the <span>(textrm{G}_{2})</span>-Laplacian flow with uniformly bounded scalar curvature is derived from the logarithmic Sobolev inequality. The uniform Sololev inequality implies a <span>(kappa )</span>-noncollapsing estimate for the <span>(textrm{G}_{2})</span>-Laplacian flow with uniformly bounded scalar curvature. Furthermore, by using the logarithmic Sobolev inequality, we prove Gaussian-type upper bounds for the heat kernel along the <span>(textrm{G}_{2})</span>-Laplacian flow with uniformly bounded scalar curvature.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Stability of Killing Cylinders in Hyperbolic Space 论双曲空间中杀圆柱体的稳定性
The Journal of Geometric Analysis Pub Date : 2024-07-01 DOI: 10.1007/s12220-024-01720-8
Antonio Bueno, Rafael López
{"title":"On the Stability of Killing Cylinders in Hyperbolic Space","authors":"Antonio Bueno, Rafael López","doi":"10.1007/s12220-024-01720-8","DOIUrl":"https://doi.org/10.1007/s12220-024-01720-8","url":null,"abstract":"<p>In this paper we study the stability of a Killing cylinder in hyperbolic 3-space when regarded as a capillary surface for the partitioning problem. In contrast with the Euclidean case, we consider a variety of totally umbilical support surfaces, including horospheres, totally geodesic planes, equidistant surfaces and round spheres. In all of them, we explicitly compute the Morse index of the corresponding eigenvalue problem for the Jacobi operator. We also address the stability of compact pieces of Killing cylinders with Dirichlet boundary conditions when the boundary is formed by two fixed circles, exhibiting an analogous to the Plateau–Rayleigh instability criterion for Killing cylinders in the Euclidean space. Finally, we prove that the Delaunay surfaces can be obtained by bifurcating Killing cylinders supported on geodesic planes.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Harmonic Morphisms from Fefferman Spaces 来自费弗曼空间的谐波变形
The Journal of Geometric Analysis Pub Date : 2024-07-01 DOI: 10.1007/s12220-024-01731-5
Sorin Dragomir, Francesco Esposito, Eric Loubeau
{"title":"Harmonic Morphisms from Fefferman Spaces","authors":"Sorin Dragomir, Francesco Esposito, Eric Loubeau","doi":"10.1007/s12220-024-01731-5","DOIUrl":"https://doi.org/10.1007/s12220-024-01731-5","url":null,"abstract":"<p>We study a ramification of a phenomenon discovered by Baird and Eells (in: Looijenga et al (eds) Geometry Symposium Utrecht 1980. Lecture Notes in Mathematics, Springer, Berlin, 1981) i.e. that non-constant harmonic morphisms <span>(Phi : {{mathfrak {M}}}^{textrm{N}} rightarrow N^2)</span> from a <span>(mathrm N)</span>-dimensional (<span>(textrm{N} ge 3)</span>) Riemannian manifold <span>({{mathfrak {M}}}^{textrm{N}})</span>, into a Riemann surface <span>(N^2)</span>, can be characterized as those horizontally weakly conformal maps having minimal fibres. We recover Baird–Eells’ result for <span>(S^1)</span> invariant harmonic morphisms <span>(Phi : {{mathfrak {M}}}^{2n+2} rightarrow N^2)</span> from a class of Lorentzian manifolds arising as total spaces <span>({{mathfrak {M}}} = C(M))</span> of canonical circle bundles <span>(S^1 rightarrow {{mathfrak {M}}} rightarrow M)</span> over strictly pseudoconvex CR manifolds <span>(M^{2n+1})</span>. The corresponding base maps <span>(phi : M^{2n+1} rightarrow N^2)</span> are shown to satisfy <span>(lim _{epsilon rightarrow 0^+} , pi _{{{mathscr {H}}}^phi } , mu ^{{{mathscr {V}}}^phi }_epsilon = 0)</span>, where <span>(mu ^{{{mathscr {V}}}^phi }_epsilon )</span> is the mean curvature vector of the vertical distribution <span>({{mathscr {V}}}^phi = textrm{Ker} (d phi ))</span> on the Riemannian manifold <span>((M, , g_epsilon ))</span>, and <span>({ g_epsilon }_{0&lt; epsilon &lt; 1})</span> is a family of contractions of the Levi form of the pseudohermitian manifold <span>((M, , theta ))</span>.\u0000</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rigidity of Free Boundary Minimal Disks in Mean Convex Three-Manifolds 平均凸三网格中自由边界最小盘的刚性
The Journal of Geometric Analysis Pub Date : 2024-06-28 DOI: 10.1007/s12220-024-01727-1
Rondinelle Batista, Barnabé Lima, João Silva
{"title":"Rigidity of Free Boundary Minimal Disks in Mean Convex Three-Manifolds","authors":"Rondinelle Batista, Barnabé Lima, João Silva","doi":"10.1007/s12220-024-01727-1","DOIUrl":"https://doi.org/10.1007/s12220-024-01727-1","url":null,"abstract":"<p>The purpose of this article is to study rigidity of free boundary minimal two-disks that locally maximize the modified Hawking mass on a Riemannian three-manifold with a positive lower bound on its scalar curvature and mean convex boundary. Assuming the strict stability of <span>(Sigma )</span>, we prove that a neighborhood of it in <i>M</i> is isometric to one of the half de Sitter–Schwarzschild space.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometric Description of Some Loewner Chains with Infinitely Many Slits 具有无限多裂缝的一些 Loewner 链的几何描述
The Journal of Geometric Analysis Pub Date : 2024-06-27 DOI: 10.1007/s12220-024-01718-2
Eleftherios K. Theodosiadis, Konstantinos Zarvalis
{"title":"Geometric Description of Some Loewner Chains with Infinitely Many Slits","authors":"Eleftherios K. Theodosiadis, Konstantinos Zarvalis","doi":"10.1007/s12220-024-01718-2","DOIUrl":"https://doi.org/10.1007/s12220-024-01718-2","url":null,"abstract":"<p>We study the chordal Loewner equation associated with certain driving functions that produce infinitely many slits. Specifically, for a choice of a sequence of positive numbers <span>((b_n)_{nge 1})</span> and points of the real line <span>((k_n)_{nge 1})</span>, we explicitily solve the Loewner PDE </p><span>$$begin{aligned} dfrac{partial f}{partial t}(z,t)=-f'(z,t)sum _{n=1}^{+infty }dfrac{2b_n}{z-k_nsqrt{1-t}} end{aligned}$$</span><p>in <span>(mathbb {H}times [0,1))</span>. Using techniques involving the harmonic measure, we analyze the geometric behaviour of its solutions, as <span>(trightarrow 1^-)</span>.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal $$L^p$$ Regularity for $$bar{partial }$$ on the Hartogs Triangle 哈托格三角形上 $$bar{partial }$$ 的最优 $$L^p$ 规律性
The Journal of Geometric Analysis Pub Date : 2024-06-27 DOI: 10.1007/s12220-024-01728-0
Yuan Zhang
{"title":"Optimal $$L^p$$ Regularity for $$bar{partial }$$ on the Hartogs Triangle","authors":"Yuan Zhang","doi":"10.1007/s12220-024-01728-0","DOIUrl":"https://doi.org/10.1007/s12220-024-01728-0","url":null,"abstract":"<p>In this paper, we prove weighted <span>(L^p)</span> estimates for the canonical solutions on product domains. As an application, we show that if <span>(pin [4, infty ))</span>, the <span>(bar{partial })</span> equation on the Hartogs triangle with <span>(L^p)</span> data admits <span>(L^p)</span> solutions with the desired estimates. For any <span>(epsilon &gt;0)</span>, by constructing an example with <span>(L^p)</span> data but having no <span>(L^{p+epsilon })</span> solutions, we verify the sharpness of the <span>(L^p)</span> regularity on the Hartogs triangle.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"124 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Areas of Genus Zero Free Boundary Minimal Surfaces Embedded in the Unit 3-Ball 论嵌入单元 3 球的零属自由边界极小曲面的面积
The Journal of Geometric Analysis Pub Date : 2024-06-27 DOI: 10.1007/s12220-024-01726-2
Peter McGrath, Jiahua Zou
{"title":"On the Areas of Genus Zero Free Boundary Minimal Surfaces Embedded in the Unit 3-Ball","authors":"Peter McGrath, Jiahua Zou","doi":"10.1007/s12220-024-01726-2","DOIUrl":"https://doi.org/10.1007/s12220-024-01726-2","url":null,"abstract":"<p>We prove that the area of each nonflat genus zero free boundary minimal surface embedded in the unit 3-ball is less than the area of its radial projection to <span>({mathbb {S}}^2)</span>. The inequality is asymptotically sharp, and we prove any sequence of surfaces saturating it converges weakly to <span>({mathbb {S}}^2)</span>, as currents and as varifolds.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"353 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Non-spin Method to the Positive Weighted Mass Theorem for Weighted Manifolds 加权流形的正加权质量定理的非自旋方法
The Journal of Geometric Analysis Pub Date : 2024-06-27 DOI: 10.1007/s12220-024-01725-3
Jianchun Chu, Jintian Zhu
{"title":"A Non-spin Method to the Positive Weighted Mass Theorem for Weighted Manifolds","authors":"Jianchun Chu, Jintian Zhu","doi":"10.1007/s12220-024-01725-3","DOIUrl":"https://doi.org/10.1007/s12220-024-01725-3","url":null,"abstract":"<p>In this paper, we investigate the weighted mass for weighted manifolds. By establishing a version of density theorem and generalizing Geroch conjecture in the setting of <i>P</i>-scalar curvature, we are able to prove the positive weighted mass theorem for weighted manifolds, which generalizes the result of Baldauf–Ozuch (Commun Math Phys 394(3):1153–1172, 2022) to non-spin manifolds.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"224 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Network Design and Control: Shape and Topology Optimization for the Turnpike Property for the Wave Equation 网络设计与控制：波方程中匝道属性的形状和拓扑优化
The Journal of Geometric Analysis Pub Date : 2024-06-27 DOI: 10.1007/s12220-024-01712-8
Martin Gugat, Meizhi Qian, Jan Sokolowski
{"title":"Network Design and Control: Shape and Topology Optimization for the Turnpike Property for the Wave Equation","authors":"Martin Gugat, Meizhi Qian, Jan Sokolowski","doi":"10.1007/s12220-024-01712-8","DOIUrl":"https://doi.org/10.1007/s12220-024-01712-8","url":null,"abstract":"<p>The optimal control problems for the wave equation are considered on networks. The turnpike property is shown for the state equation, the adjoint state equation as well as the optimal cost. The shape and topology optimization is performed for the network with the shape functional given by the optimality system of the control problem. The set of admissible shapes for the network is compact in finite dimensions, thus the use of turnpike property is straightforward. The topology optimization is analysed for an example of nucleation of a small cycle at the internal node of network. The topological derivative of the cost is introduced and evaluated in the framework of domain decomposition technique. Numerical examples are provided.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hardy-Littlewood Type Theorems and a Hopf Type Lemma 哈代-利特尔伍德类型定理和霍普夫类型定理
The Journal of Geometric Analysis Pub Date : 2024-06-27 DOI: 10.1007/s12220-024-01717-3
Shaolin Chen, Hidetaka Hamada, Dou Xie
{"title":"Hardy-Littlewood Type Theorems and a Hopf Type Lemma","authors":"Shaolin Chen, Hidetaka Hamada, Dou Xie","doi":"10.1007/s12220-024-01717-3","DOIUrl":"https://doi.org/10.1007/s12220-024-01717-3","url":null,"abstract":"<p>The main aim of this paper is to investigate Hardy-Littlewood type Theorems and a Hopf type lemma on functions induced by a differential operator. We first prove more general Hardy-Littlewood type theorems for the Dirichlet solution of a differential operator which depends on <span>(alpha in (-1,infty ))</span> over the unit ball <span>(mathbb {B}^n)</span> of <span>(mathbb {R}^n)</span> with <span>(nge 2)</span>, related to the Lipschitz type space defined by a majorant which satisfies some assumption. We find that the case <span>(alpha in (0,infty ))</span> is completely different from the case <span>(alpha =0)</span> due to Dyakonov (Adv. Math. 187 (2004), 146–172). Then a more general Hopf type lemma for the Dirichlet solution of a differential operator will also be established in the case <span>(alpha &gt;n-2)</span>.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"83 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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