Existence of harmonic maps into CAT(1) spaces

被引：0

作者：

Breiner, Christine ^{[1
]}

Fraser, Ailana ^{[2
]}

Huang, Lan-Hsuan ^{[3
]}

Mese, Chikako ^{[4
]}

Sargent, Pam ^{[5
]}

Zhang, Yingying ^{[6
]}

机构：

[1] Fordham Univ, Dept Math, Bronx, NY 10458 USA

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[3] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[4] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

[5] York Univ, Dept Math & Stat, Toronto, ON M3J 13P, Canada

[6] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

来源：

COMMUNICATIONS IN ANALYSIS AND GEOMETRY | 2020年 / 28卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

MINIMAL IMMERSIONS; MAPPINGS; MANIFOLDS; SURFACES; BUNDLES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let phi is an element of C-0 boolean AND W-1,W-2(Sigma,X) where Sigma is a compact Riemann surface, X is a compact locally CAT(1) space, and W-1,W-2(Sigma,X) is defined as in Korevaar-Schoen. We use the technique of harmonic replacement to prove that either there exists a harmonic map u : Sigma -> X homotopic to phi or there exists a nontrivial conformal harmonic map v : S-2 -> X. To complete the argument, we prove compactness for energy minimizers and a removable singularity theorem for conformal harmonic maps.

引用

页码：781 / 835

页数：55

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