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Differential Geometry and its Applications最新文献

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Lower estimates for the length of the second fundamental form of submanifolds
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-02-01 DOI: 10.1016/j.difgeo.2024.102216
Francisco G.S. Carvalho , Barnabé P. Lima , Paulo A. Sousa , Bruno V.M. Vieira
{"title":"Lower estimates for the length of the second fundamental form of submanifolds","authors":"Francisco G.S. Carvalho ,&nbsp;Barnabé P. Lima ,&nbsp;Paulo A. Sousa ,&nbsp;Bruno V.M. Vieira","doi":"10.1016/j.difgeo.2024.102216","DOIUrl":"10.1016/j.difgeo.2024.102216","url":null,"abstract":"<div><div>In a remarkable work <span><span>[35]</span></span>, Wei established estimates for the eigenvalues of the Laplacian on closed submanifolds <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> embedded in a unit sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>+</mo><mi>m</mi></mrow></msup></math></span>. In this study, we extend these results to the eigenvalues of the <em>p</em>-Laplacian. As a consequence, we provide new characterizations of the sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. Additionally, we derive integral inequalities in terms of the norm of the second fundamental form of <em>M</em> and the first non-zero eigenvalue of the <em>p</em>-Laplacian, thereby generalizing the results previously established by Santos and Soares <span><span>[11]</span></span> for hypersurfaces.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102216"},"PeriodicalIF":0.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Gradient estimates of a nonlinear parabolic equation under integral Bakry-Émery Ricci condition
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-02-01 DOI: 10.1016/j.difgeo.2024.102222
Xavier Ramos Olivé , Shoo Seto
{"title":"Gradient estimates of a nonlinear parabolic equation under integral Bakry-Émery Ricci condition","authors":"Xavier Ramos Olivé ,&nbsp;Shoo Seto","doi":"10.1016/j.difgeo.2024.102222","DOIUrl":"10.1016/j.difgeo.2024.102222","url":null,"abstract":"<div><div>We prove a global gradient estimate to positive solutions of the nonlinear parabolic equation <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>f</mi></mrow></msub><mi>u</mi><mo>+</mo><mi>a</mi><mi>u</mi><mi>ln</mi><mo>⁡</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>+</mo><mi>b</mi><mi>u</mi></math></span> under an integral Bakry-Émery Ricci condition on compact weighted manifolds. The elliptic version of the equation arises in the study of gradient Ricci solitons and in this paper we consider the parabolic version.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102222"},"PeriodicalIF":0.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A global invariant for path structures and second order differential equations
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-02-01 DOI: 10.1016/j.difgeo.2024.102224
E. Falbel , J.M. Veloso
{"title":"A global invariant for path structures and second order differential equations","authors":"E. Falbel ,&nbsp;J.M. Veloso","doi":"10.1016/j.difgeo.2024.102224","DOIUrl":"10.1016/j.difgeo.2024.102224","url":null,"abstract":"<div><div>We study a global invariant for path structures which is obtained as a secondary invariant from a Cartan connection on a canonical bundle associated to a path structure. This invariant is computed in examples which are defined in terms of reductions of the path structure. In particular we give a formula for this global invariant for second order differential equations defined on a torus <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102224"},"PeriodicalIF":0.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Ricci flow of discrete surfaces of revolution, and relation to constant Gaussian curvature
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-02-01 DOI: 10.1016/j.difgeo.2024.102221
Naoya Suda
{"title":"Ricci flow of discrete surfaces of revolution, and relation to constant Gaussian curvature","authors":"Naoya Suda","doi":"10.1016/j.difgeo.2024.102221","DOIUrl":"10.1016/j.difgeo.2024.102221","url":null,"abstract":"<div><div>Giving explicit parametrizations of discrete constant Gaussian curvature surfaces of revolution that are defined from an integrable systems approach, we study Ricci flow for discrete surfaces, and see how discrete surfaces of revolution have a geometric realization for the Ricci flow that approaches the constant Gaussian curvature surfaces we have parametrized.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102221"},"PeriodicalIF":0.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Rigidity of closed vacuum static spaces
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-02-01 DOI: 10.1016/j.difgeo.2024.102217
Guangyue Huang, Qi Guo, Bingqing Ma
{"title":"Rigidity of closed vacuum static spaces","authors":"Guangyue Huang,&nbsp;Qi Guo,&nbsp;Bingqing Ma","doi":"10.1016/j.difgeo.2024.102217","DOIUrl":"10.1016/j.difgeo.2024.102217","url":null,"abstract":"<div><div>In this paper, we study the rigidity results of closed vacuum static spaces. By introducing a trace-free three tensor, we provide a necessary condition that such spaces with the dimensional scope <span><math><mn>3</mn><mo>≤</mo><mi>n</mi><mo>≤</mo><mn>5</mn></math></span> must be of Einstein.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102217"},"PeriodicalIF":0.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Subgradient estimates for the equation Δbu+aulog⁡u+bu=0 on complete noncompact pseudo-Hermitian manifolds
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-02-01 DOI: 10.1016/j.difgeo.2024.102223
Biqiang Zhao
{"title":"Subgradient estimates for the equation Δbu+aulog⁡u+bu=0 on complete noncompact pseudo-Hermitian manifolds","authors":"Biqiang Zhao","doi":"10.1016/j.difgeo.2024.102223","DOIUrl":"10.1016/j.difgeo.2024.102223","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>H</mi><mi>M</mi><mo>,</mo><mi>J</mi><mo>,</mo><mi>θ</mi><mo>)</mo></math></span> be a complete pseudo-Hermitian (2m+1)-manifold. In this paper, we derive the subgradient estimates for the positive solutions of the equation <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>b</mi></mrow></msub><mi>u</mi><mo>+</mo><mi>a</mi><mi>u</mi><mi>log</mi><mo>⁡</mo><mi>u</mi><mo>+</mo><mi>b</mi><mi>u</mi><mo>=</mo><mn>0</mn></math></span> on complete noncompact pseudo-Hermitian manifolds without the commutation condition.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102223"},"PeriodicalIF":0.6,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Deformation rigidity of the double Cayley Grassmannian
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-01-31 DOI: 10.1016/j.difgeo.2024.102219
Shin-young Kim , Kyeong-Dong Park
{"title":"Deformation rigidity of the double Cayley Grassmannian","authors":"Shin-young Kim ,&nbsp;Kyeong-Dong Park","doi":"10.1016/j.difgeo.2024.102219","DOIUrl":"10.1016/j.difgeo.2024.102219","url":null,"abstract":"<div><div>The double Cayley Grassmannian is a unique smooth equivariant completion with Picard number one of the 14-dimensional exceptional complex Lie group <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, and it parametrizes eight-dimensional isotropic subalgebras of the complexified bi-octonions. We show the rigidity of the double Cayley Grassmannian under Kähler deformations. This means that for any smooth projective family of complex manifolds over a connected base of which one fiber is biholomorphic to the double Cayley Grassmannian, all other fibers are biholomorphic to the double Cayley Grassmannian.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102219"},"PeriodicalIF":0.6,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143101467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Spacelike foliations on Lorentz manifolds
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-01-31 DOI: 10.1016/j.difgeo.2025.102235
Aldir Brasil , Sharief Deshmukh , Euripedes da Silva , Paulo Sousa
{"title":"Spacelike foliations on Lorentz manifolds","authors":"Aldir Brasil ,&nbsp;Sharief Deshmukh ,&nbsp;Euripedes da Silva ,&nbsp;Paulo Sousa","doi":"10.1016/j.difgeo.2025.102235","DOIUrl":"10.1016/j.difgeo.2025.102235","url":null,"abstract":"<div><div>In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We investigate conditions for the leaves being stable, totally geodesic or totally umbilical. We consider that <span><math><msup><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> is equipped with a timelike closed conformal vector field <em>ξ</em>. If the foliation has constant mean curvature, we show that the leaves are stable. When the leaves are compact spacelike hypersurfaces we show that, under certain conditions, its are totally umbilic hypersurfaces. In the case of foliations by complete noncompact hypersurfaces, we using a Maximum Principle at infinity to conclude that the foliation is totally geodesic.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102235"},"PeriodicalIF":0.6,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143101468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Diameter theorems on Kähler and quaternionic Kähler manifolds under a positive lower curvature bound 正下曲率界下Kähler和四元数Kähler流形的直径定理
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-11-29 DOI: 10.1016/j.difgeo.2024.102218
Maria Gordina , Gunhee Cho
{"title":"Diameter theorems on Kähler and quaternionic Kähler manifolds under a positive lower curvature bound","authors":"Maria Gordina ,&nbsp;Gunhee Cho","doi":"10.1016/j.difgeo.2024.102218","DOIUrl":"10.1016/j.difgeo.2024.102218","url":null,"abstract":"<div><div>We define the orthogonal Bakry-Émery tensor as a generalization of the orthogonal Ricci curvature, and then study diameter theorems on Kähler and quaternionic Kähler manifolds under positivity assumption on the orthogonal Bakry-Émery tensor. Moreover, under such assumptions on the orthogonal Bakry-Émery tensor and the holomorphic or quaternionic sectional curvature on a Kähler manifold or a quaternionic Kähler manifold respectively, the Bonnet-Myers type diameter bounds are sharper than in the Riemannian case.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102218"},"PeriodicalIF":0.6,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142746975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Integral Ricci curvature bounds for possibly collapsed spaces with Ricci curvature bounded from below 里奇曲率自下而上有界的可能坍缩空间的里奇曲率积分界值
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2024-11-21 DOI: 10.1016/j.difgeo.2024.102214
Michael Smith
{"title":"Integral Ricci curvature bounds for possibly collapsed spaces with Ricci curvature bounded from below","authors":"Michael Smith","doi":"10.1016/j.difgeo.2024.102214","DOIUrl":"10.1016/j.difgeo.2024.102214","url":null,"abstract":"<div><div>Assuming a lower bound on the Ricci curvature of a complete Riemannian manifold, for <span><math><mi>q</mi><mo>&lt;</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span> we show the existence of bounds on the local <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span> norm of the Ricci curvature that depend only on the dimension and which improve with volume collapse.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"98 ","pages":"Article 102214"},"PeriodicalIF":0.6,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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