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Conformal solitons for the mean curvature flow in hyperbolic space 双曲空间平均曲率流的共形孤子
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-03-15 DOI: 10.1007/s10455-024-09947-y
L. Mari, J. Rocha de Oliveira, A. Savas-Halilaj, R. Sodré de Sena
{"title":"Conformal solitons for the mean curvature flow in hyperbolic space","authors":"L. Mari,&nbsp;J. Rocha de Oliveira,&nbsp;A. Savas-Halilaj,&nbsp;R. Sodré de Sena","doi":"10.1007/s10455-024-09947-y","DOIUrl":"10.1007/s10455-024-09947-y","url":null,"abstract":"<div><p>In this paper, we study conformal solitons for the mean curvature flow in hyperbolic space <span>(mathbb {H}^{n+1})</span>. Working in the upper half-space model, we focus on horo-expanders, which relate to the conformal field <span>(-partial _0)</span>. We classify cylindrical and rotationally symmetric examples, finding appropriate analogues of grim-reaper cylinders, bowl and winglike solitons. Moreover, we address the Plateau and the Dirichlet problems at infinity. For the latter, we provide the sharp boundary convexity condition to guarantee its solvability and address the case of non-compact boundaries contained between two parallel hyperplanes of <span>(partial _infty mathbb {H}^{n+1})</span>. We conclude by proving rigidity results for bowl and grim-reaper cylinders.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09947-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140147557","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
Multiple tubular excisions and large Steklov eigenvalues 多重管状切除和大斯特克洛夫特征值
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-03-10 DOI: 10.1007/s10455-024-09949-w
Jade Brisson
{"title":"Multiple tubular excisions and large Steklov eigenvalues","authors":"Jade Brisson","doi":"10.1007/s10455-024-09949-w","DOIUrl":"10.1007/s10455-024-09949-w","url":null,"abstract":"<div><p>Given a closed Riemannian manifold <i>M</i> and <span>(bge 2)</span> closed connected submanifolds <span>(N_jsubset M)</span> of codimension at least 2, we prove that the first nonzero eigenvalue of the domain <span>(Omega _varepsilon subset M)</span> obtained by removing the tubular neighbourhood of size <span>(varepsilon )</span> around each <span>(N_j)</span> tends to infinity as <span>(varepsilon )</span> tends to 0. More precisely, we prove a lower bound in terms of <span>(varepsilon )</span>, <i>b</i>, the geometry of <i>M</i> and the codimensions and the volumes of the submanifolds and an upper bound in terms of <span>(varepsilon )</span> and the codimensions of the submanifolds. For eigenvalues of index <span>(k=b,b+1,ldots )</span>, we have a stronger result: their order of divergence is <span>(varepsilon ^{-1})</span> and their rate of divergence is only depending on <i>m</i> and on the codimensions of the submanifolds.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09949-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099898","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
Rigidity results of weighted area-minimizing hypersurfaces 加权面积最小超曲面的刚性结果
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-03-05 DOI: 10.1007/s10455-024-09948-x
Sanghun Lee, Sangwoo Park, Juncheol Pyo
{"title":"Rigidity results of weighted area-minimizing hypersurfaces","authors":"Sanghun Lee,&nbsp;Sangwoo Park,&nbsp;Juncheol Pyo","doi":"10.1007/s10455-024-09948-x","DOIUrl":"10.1007/s10455-024-09948-x","url":null,"abstract":"<div><p>In this paper, we prove two rigidity results of hypersurfaces in <i>n</i>-dimensional weighted Riemannian manifolds with weighted scalar curvature bounded from below. Firstly, we establish a splitting theorem for the <i>n</i>-dimensional weighted Riemannian manifold via a weighted area-minimizing hypersurface. Secondly, we observe the topological invariance of the weighted stable hypersurface when the ambient weighted scalar curvature is bounded from below by a positive constant. In particular, we derive a non-existence result for a weighted stable hypersurface.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140044142","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
Correction to: Hypercohomologies of truncated twisted holomorphic de Rham complexes Correction to：截断扭曲全态德拉姆复合物的超同调
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-02-29 DOI: 10.1007/s10455-024-09944-1
Lingxu Meng
{"title":"Correction to: Hypercohomologies of truncated twisted holomorphic de Rham complexes","authors":"Lingxu Meng","doi":"10.1007/s10455-024-09944-1","DOIUrl":"10.1007/s10455-024-09944-1","url":null,"abstract":"","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140004343","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
Some regularity of submetries 子网格的某些规律性
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-02-21 DOI: 10.1007/s10455-024-09946-z
Alexander Lytchak
{"title":"Some regularity of submetries","authors":"Alexander Lytchak","doi":"10.1007/s10455-024-09946-z","DOIUrl":"10.1007/s10455-024-09946-z","url":null,"abstract":"<div><p>We discuss regularity statements for equidistant decompositions of Riemannian manifolds and for the corresponding quotient spaces. We show that any stratum of the quotient space has curvature locally bounded from both sides.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09946-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139949164","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
Subgraphs of BV functions on RCD spaces RCD 空间上的 BV 函数子图
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-02-17 DOI: 10.1007/s10455-024-09945-0
Gioacchino Antonelli, Camillo Brena, Enrico Pasqualetto
{"title":"Subgraphs of BV functions on RCD spaces","authors":"Gioacchino Antonelli,&nbsp;Camillo Brena,&nbsp;Enrico Pasqualetto","doi":"10.1007/s10455-024-09945-0","DOIUrl":"10.1007/s10455-024-09945-0","url":null,"abstract":"<div><p>In this work, we extend classical results for subgraphs of functions of bounded variation in <span>(mathbb R^ntimes mathbb R)</span> to the setting of <span>({textsf{X}}times mathbb R)</span>, where <span>({textsf{X}})</span> is an <span>({textrm{RCD}}(K,N))</span> metric measure space. In particular, we give the precise expression of the push-forward onto <span>({textsf{X}})</span> of the perimeter measure of the subgraph in <span>({textsf{X}}times mathbb R)</span> of a <span>({textrm{BV}})</span> function on <span>({textsf{X}})</span>. Moreover, in properly chosen good coordinates, we write the precise expression of the normal to the boundary of the subgraph of a <span>({textrm{BV}})</span> function <i>f</i> with respect to the polar vector of <i>f</i>, and we prove change-of-variable formulas.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09945-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139768560","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
Some remarks on almost Hermitian functionals 关于几乎赫尔墨斯函数的一些评论
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-01-31 DOI: 10.1007/s10455-023-09943-8
Tedi Draghici, Cem Sayar
{"title":"Some remarks on almost Hermitian functionals","authors":"Tedi Draghici,&nbsp;Cem Sayar","doi":"10.1007/s10455-023-09943-8","DOIUrl":"10.1007/s10455-023-09943-8","url":null,"abstract":"<div><p>We study critical points of natural functionals on various spaces of almost Hermitian structures on a compact manifold <span>(M^{2n})</span>. We present a general framework, introducing the notion of gradient of an almost Hermitian functional. As a consequence of the diffeomorphism invariance, we show that a Schur’s type theorem still holds for general almost Hermitian functionals, generalizing a known fact for Riemannian functionals. We present two concrete examples, the Gauduchon’s functional and a close relative of it. These functionals have been studied previously, but not in the most general setup as we do here, and we make some new observations about their critical points.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139647779","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 subelliptic harmonic maps with potential 关于有潜力的亚椭圆谐波映射
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-01-30 DOI: 10.1007/s10455-023-09942-9
Yuxin Dong, Han Luo, Weike Yu
{"title":"On subelliptic harmonic maps with potential","authors":"Yuxin Dong,&nbsp;Han Luo,&nbsp;Weike Yu","doi":"10.1007/s10455-023-09942-9","DOIUrl":"10.1007/s10455-023-09942-9","url":null,"abstract":"<div><p>Let <span>((M,H,g_H;g))</span> be a sub-Riemannian manifold and (<i>N</i>, <i>h</i>) be a Riemannian manifold. For a smooth map <span>(u: M rightarrow N)</span>, we consider the energy functional <span>(E_G(u) = frac{1}{2} int _M[|textrm{d}u_text {H}|^2 - 2,G(u)] textrm{d}V_M)</span>, where <span>(textrm{d}u_text {H})</span> is the horizontal differential of <i>u</i>, <span>(G:Nrightarrow mathbb {R})</span> is a smooth function on <i>N</i>. The critical maps of <span>(E_G(u))</span> are referred to as subelliptic harmonic maps with potential <i>G</i>. In this paper, we investigate the existence problem for subelliptic harmonic maps with potentials by a subelliptic heat flow. Assuming that the target Riemannian manifold has nonpositive sectional curvature and the potential <i>G</i> satisfies various suitable conditions, we prove some Eells–Sampson-type existence results when the source manifold is either a step-2 sub-Riemannian manifold or a step-<i>r</i> sub-Riemannian manifold whose sub-Riemannian structure comes from a tense Riemannian foliation.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139648081","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
Almost CR manifolds with contracting CR automorphism 几乎 CR 流形的收缩 CR 自定态
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-01-23 DOI: 10.1007/s10455-023-09941-w
Jae-Cheon Joo, Kang-Hyurk Lee
{"title":"Almost CR manifolds with contracting CR automorphism","authors":"Jae-Cheon Joo,&nbsp;Kang-Hyurk Lee","doi":"10.1007/s10455-023-09941-w","DOIUrl":"10.1007/s10455-023-09941-w","url":null,"abstract":"<div><p>In this paper, we deal with a strongly pseudoconvex almost CR manifold with a CR contraction. We will prove that the stable manifold of the CR contraction is CR equivalent to the Heisenberg group model.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139556531","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
Instability of a family of examples of harmonic maps 谐波映射实例族的不稳定性
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-01-09 DOI: 10.1007/s10455-023-09936-7
Nobumitsu Nakauchi
{"title":"Instability of a family of examples of harmonic maps","authors":"Nobumitsu Nakauchi","doi":"10.1007/s10455-023-09936-7","DOIUrl":"10.1007/s10455-023-09936-7","url":null,"abstract":"<div><p>The radial map <i>u</i>(<i>x</i>) <span>(=)</span> <span>(frac{x}{Vert xVert })</span> is a well-known example of a harmonic map from <span>({mathbb {R}}^m,-,{0})</span> into the spheres <span>({mathbb {S}}^{m-1})</span> with a point singularity at <i>x</i> <span>(=)</span> 0. In Nakauchi (Examples Counterexamples 3:100107, 2023), the author constructed recursively a family of harmonic maps <span>(u^{(n)})</span> into <span>({mathbb {S}}^{m^n-1})</span> with a point singularity at the origin <span>((n = 1,,2,ldots ))</span>, such that <span>(u^{(1)})</span> is the above radial map. It is known that for <i>m</i> <span>(ge )</span> 3, the radial map <span>(u^{(1)})</span> is not only <i>stable</i> as a harmonic map but also a <i>minimizer</i> of the energy of harmonic maps. In this paper, we show that for <i>n</i> <span>(ge )</span> 2, <span>(u^{(n)})</span> may be <i>unstable</i> as a harmonic map. Indeed we prove that under the assumption <i>n</i> &gt; <span>({displaystyle frac{sqrt{3}-1}{2},(m-1)})</span> <span>((m ge 3)</span>, <span>(n ge 2))</span>, the map <span>(u^{(n)})</span> is <i>unstable</i> as a harmonic map. It is remarkable that they are unstable and our result gives many examples of <i>unstable</i> harmonic maps into the spheres with a point singularity at the origin.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139410564","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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