LIOUVILLE THEOREM FOR HARMONIC MAPS FROM RIEMANNIAN MANIFOLD WITH COMPACT BOUNDARY

被引：0

作者：

Sun, Jun ^{[1
,2
]}

Zhu, Xiaobao ^{[3
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[2] Wuhan Univ, Hubei Key Lab Computat Sci, Wuhan 430072, Peoples R China

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

来源：

KODAI MATHEMATICAL JOURNAL | 2023年 / 46卷 / 02期

关键词：

Liouville theorem; gradient estimate; harmonic maps; RICCI CURVATURE;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note we will provide a gradient estimate for harmonic maps from a complete noncompact Riemannian manifold with compact boundary (which we call "Kasue manifold") into a simply connected complete Riemannian manifold with non-positive sectional curvature. As a consequence, we can obtain a Liouville theorem. We will also show the nonexistence of positive solutions to some linear elliptic equations on Kasue manifolds.

引用

页码：207 / 218

页数：12

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