Liouville Theorem for harmonic maps from Riemannian manifold with compact boundary

IF 0.4 4区 数学 Q4 MATHEMATICS
Jun Sun, Xiaobao Zhu
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引用次数: 0

Abstract

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 equation on Kasue manifold.
紧致边界黎曼流形调和映射的Liouville定理
本文给出了边界紧致的完全非紧黎曼流形(我们称之为“Kasue流形”)到截面曲率非正的单连通完全黎曼流形调和映射的梯度估计。因此,我们可以得到一个刘维尔定理。我们还将证明Kasue流形上某些线性椭圆方程正解的不存在性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: Kodai Mathematical Journal is edited by the Department of Mathematics, Tokyo Institute of Technology. The journal was issued from 1949 until 1977 as Kodai Mathematical Seminar Reports, and was renewed in 1978 under the present name. The journal is published three times yearly and includes original papers in mathematics.
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