The Refined Analysis on the Convergence Behavior of Harmonic Map Sequence from Cylinders

被引：10

作者：

Chen, Li ^{[1
]}

Li, Yuxiang ^{[2
]}

Wang, Youde ^{[1
]}

机构：

[1] Chinese Acad Sci, Acad Math & Systemat Sci, Beijing 100190, Peoples R China

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2012年 / 22卷 / 04期

基金：

美国国家科学基金会;

关键词：

Harmonic map; Blow up; Geodesic; MANIFOLDS; EVOLUTION; MAPPINGS; SURFACES;

D O I：

10.1007/s12220-011-9222-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we are concerned with the convergence behavior of a sequence of harmonic maps from long cylinders with uniformly bounded energy. If the bubbling phenomenon does not occur, we give the length formula of the limit map (i.e., geodesic in the target manifold). Furthermore, we provide a geometric explanation of the energy identity for a sequence of harmonic maps from degenerating Riemann surfaces with uniformly bounded energy, proved by M. Zhu.

引用

页码：942 / 963

页数：22

共 18 条

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