Partial Regularity of Harmonic Maps From Alexandrov Spaces

被引：0

作者：

Ge, Huabin ^{[1
]}

Jiang, Wenshuai ^{[2
]}

Zhang, Hui-Chun ^{[3
]}

机构：

[1] Renmin Univ China, Sch Math, Beijing 100872, Peoples R China

[2] Zhejiang Univ, Sch Math Sci, Hangzhou 310058, Peoples R China

[3] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Peoples R China

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2022年 / 2022卷 / 15期

基金：

中国国家自然科学基金;

关键词：

LOCAL DIRICHLET SPACES; METRIC MEASURE-SPACES; SINGULAR SPACES; SOBOLEV SPACES; HEAT KERNEL; STATIONARY; MAPPINGS;

D O I：

10.1093/imrn/rnab074

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove the Lipschitz regularity of continuous harmonic maps from a finite-dimensional Alexandrov space to a compact smooth Riemannian manifold. This solves a conjecture of F. H. Lin in []. The proof extends the argument of Huang-Wang [].

引用

页码：11575 / 11601

页数：27

共 59 条

[1] Alexander S, 2022, Arxiv, DOI arXiv:1903.08539
[2] Ambrosio L, 2016, J GEOM ANAL, V26, P24, DOI 10.1007/s12220-014-9537-7
[3] Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
Ambrosio, Luigi
Gigli, Nicola
Savare, Giuseppe
[J]. INVENTIONES MATHEMATICAE, 2014, 195 (02) : 289 - 391
[4] On the Differential Structure of Metric Measure Spaces and Applications
不详
[J]. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 236 (1113) : 1 - +
[5] ON THE SINGULAR SET OF STATIONARY HARMONIC MAPS
BETHUEL, F
[J]. MANUSCRIPTA MATHEMATICA, 1993, 78 (04) : 417 - 443
[6] Regularity of harmonic maps from polyhedra to CAT(1) spaces
Breiner, Christine
Fraser, Ailana
Huang, Lan-Hsuan
Mese, Chikako
Sargent, Pam
Zhang, Yingying
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2018, 57 (01)
[7] Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows
Brue, Elia
Semola, Daniele
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2020, 73 (06) : 1141 - 1204
[8] Burago D, 2001, GRADUATE STUDIES MAT, V33, DOI [DOI 10.1090/GSM/033, 10.1090/gsm/033]
[9] ALEXANDROV,A.D. SPACES WITH CURVATURE BOUNDED BELOW
BURAGO, Y
GROMOV, M
PERELMAN, G
[J]. RUSSIAN MATHEMATICAL SURVEYS, 1992, 47 (02) : 1 - 58
[10] Chang SYA, 1999, COMMUN PUR APPL MATH, V52, P1099, DOI 10.1002/(SICI)1097-0312(199909)52:9<1099::AID-CPA3>3.0.CO

← 1 2 3 4 5 6 →