Differential Geometry and its Applications最新文献_第2页

Rigidity of closed minimal hypersurfaces in S5 S5中闭极小超曲面的刚性

IF 0.6 4区数学

Differential Geometry and its Applications Pub Date : 2025-05-09 DOI: 10.1016/j.difgeo.2025.102252

Pengpeng Cheng, Tongzhu Li

引用次数: 0

The strong Diederich-Fornæss index on C2 domains in Hermitian manifolds 厄米流形中C2域上的强Diederich-Fornæss指标

IF 0.6 4区数学

Differential Geometry and its Applications Pub Date : 2025-04-24 DOI: 10.1016/j.difgeo.2025.102251

Phillip S. Harrington

{"title":"The strong Diederich-Fornæss index on C2 domains in Hermitian manifolds","authors":"Phillip S. Harrington","doi":"10.1016/j.difgeo.2025.102251","DOIUrl":"10.1016/j.difgeo.2025.102251","url":null,"abstract":"<div><div>For a relatively compact Stein domain Ω with <math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math> boundary in a Hermitian manifold M, we consider the strong Diederich-Fornæss index, denoted <math><mi>D</mi><mi>F</mi><mo>(</mo><mi>Ω</mi><mo>)</mo></math>: the supremum of all exponents <math><mn>0</mn><mo><</mo><mi>η</mi><mo><</mo><mn>1</mn></math> such that eigenvalues of the complex Hessian of <math><mo>−</mo><msup><mrow><mo>(</mo><mo>−</mo><mi>ρ</mi><mo>)</mo></mrow><mrow><mi>η</mi></mrow></msup></math> are bounded below by some positive multiple of <math><msup><mrow><mo>(</mo><mo>−</mo><mi>ρ</mi><mo>)</mo></mrow><mrow><mi>η</mi></mrow></msup></math> on Ω for some <math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math> defining function ρ. We will show that <math><mi>D</mi><mi>F</mi><mo>(</mo><mi>Ω</mi><mo>)</mo></math> is completely characterized by the existence of a Hermitian metric with curvature terms satisfying a certain inequality when restricted to the null-space of the Levi-form.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102251"},"PeriodicalIF":0.6,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869102","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

The geometric Toda equations for noncompact symmetric spaces 非紧致对称空间的几何Toda方程

IF 0.6 4区数学

Differential Geometry and its Applications Pub Date : 2025-04-16 DOI: 10.1016/j.difgeo.2025.102249

Ian McIntosh

{"title":"The geometric Toda equations for noncompact symmetric spaces","authors":"Ian McIntosh","doi":"10.1016/j.difgeo.2025.102249","DOIUrl":"10.1016/j.difgeo.2025.102249","url":null,"abstract":"<div><div>This paper has two purposes. The first is to classify all those versions of the Toda equations which govern the existence of τ-primitive harmonic maps from a surface into a homogeneous space <math><mi>G</mi><mo>/</mo><mi>T</mi></math> for which G is a noncomplex noncompact simple real Lie group, τ is the Coxeter automorphism which Drinfel'd & Sokolov assigned to each affine Dynkin diagram, and T is the compact torus fixed pointwise by τ. Here τ may be either an inner or an outer automorphism. We interpret the Toda equations over a compact Riemann surface Σ as equations for a metric on a holomorphic principal <math><msup><mrow><mi>T</mi></mrow><mrow><mi>C</mi></mrow></msup></math>-bundle <math><msup><mrow><mi>Q</mi></mrow><mrow><mi>C</mi></mrow></msup></math> over Σ whose Chern connection, when combined with a holomorphic field φ, produces a G-connection which is flat precisely when the Toda equations hold. The second purpose is to establish when stability criteria for the pair <math><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mi>C</mi></mrow></msup><mo>,</mo><mi>φ</mi><mo>)</mo></math> can be used to prove the existence of solutions. We classify those real forms of the Toda equations for which this pair is a principal pair and we call these totally noncompact Toda pairs: stability theory then gives algebraic conditions for the existence of solutions. Every solution to the geometric Toda equations has a corresponding G-Higgs bundle. We explain how to construct this G-Higgs bundle directly from the Toda pair and show that Baraglia's cyclic Higgs bundles arise from a very special case of totally noncompact cyclic Toda pairs.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102249"},"PeriodicalIF":0.6,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143835095","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

Bour's theorem for helicoidal surfaces with singularities 带奇点的螺旋曲面的小时定理

IF 0.6 4区数学

Differential Geometry and its Applications Pub Date : 2025-04-03 DOI: 10.1016/j.difgeo.2025.102248

Yuki Hattori , Atsufumi Honda , Tatsuya Morimoto

引用次数: 0

The manifold of polygons degenerated to segments 多边形的流形退化为线段

IF 0.6 4区数学

Differential Geometry and its Applications Pub Date : 2025-04-01 DOI: 10.1016/j.difgeo.2025.102247

Manuel A. Espinosa-García , Ahtziri González , Yesenia Villicaña-Molina

引用次数: 0

Regulated curves on a Banach manifold and singularities of endpoint map. I. Banach manifold structure Banach流形上的调节曲线及端点映射的奇异性。1 .巴拿赫流形结构

IF 0.6 4区数学

Differential Geometry and its Applications Pub Date : 2025-03-27 DOI: 10.1016/j.difgeo.2025.102245

Tomasz Goliński , Fernand Pelletier

引用次数: 0

Solitons of the mean curvature flow in S2×R 平均曲率的孤子流在S2×R

IF 0.6 4区数学

Differential Geometry and its Applications Pub Date : 2025-03-25 DOI: 10.1016/j.difgeo.2025.102243

Rafael López , Marian Ioan Munteanu

引用次数: 0

Mean curvature flow with pinched curvature integral 带压缩曲率积分的平均曲率流

IF 0.6 4区数学

Differential Geometry and its Applications Pub Date : 2025-03-21 DOI: 10.1016/j.difgeo.2025.102244

Yongheng Han

引用次数: 0

Higher-power harmonic maps, instantons and Yang-Mills theory 高功率谐波映射，瞬子和杨-米尔斯理论

IF 0.6 4区数学

Differential Geometry and its Applications Pub Date : 2025-03-09 DOI: 10.1016/j.difgeo.2025.102240

Elias Knack, Henrik Naujoks

{"title":"Higher-power harmonic maps, instantons and Yang-Mills theory","authors":"Elias Knack, Henrik Naujoks","doi":"10.1016/j.difgeo.2025.102240","DOIUrl":"10.1016/j.difgeo.2025.102240","url":null,"abstract":"<div><div>Let <math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math> and <math><mo>(</mo><mi>N</mi><mo>,</mo><mi>h</mi><mo>)</mo></math> be two pseudo-Riemannian manifolds. We study field theoretic properties of higher-power harmonic maps (also called r-harmonic maps) <math><mi>φ</mi><mo>:</mo><mi>M</mi><mo>→</mo><mi>N</mi></math>, which are a natural generalization of standard harmonic maps first introduced by C. Wood. In particular, we discuss the coupled system of higher-power harmonic maps and the Einstein-Hilbert action and prove a sufficient condition for a map to be r-harmonic, which is highly motivated by classical field equations like the harmonic map equation or the Yang-Mills equation. Furthermore, we derive an instanton theory for r-harmonic maps on 2r-dimensional base manifolds and investigate conformal properties of general higher-power harmonic maps. Finally, since the theory of higher-power harmonic maps bears striking similarities with Yang-Mills theory, we provide a comprehensive comparison between the two theories which explains in more detail surprisingly many analogies.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102240"},"PeriodicalIF":0.6,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580361","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

Ramification and unicity theorems for Gauss maps of complete space-like stationary surfaces in four-dimensional Lorentz-Minkowski space 四维洛伦兹-闵可夫斯基空间中完全类空固定曲面高斯映射的分支和唯一性定理

IF 0.6 4区数学

Differential Geometry and its Applications Pub Date : 2025-02-27 DOI: 10.1016/j.difgeo.2025.102238

Li Ou

引用次数: 0