Non existence of quasi-harmonic spheres

被引：12

作者：

Li, Jiayu ^{[1
,2
]}

Zhu, Xiangrong ^{[1
]}

机构：

[1] Abdus Salam Int Ctr Theoret Phys, Math Grp, I-34100 Trieste, Italy

[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2010年 / 37卷 / 3-4期

关键词：

SELF-SIMILAR SOLUTIONS; HEAT FLOWS; BLOW-UP; MAPS;

D O I：

10.1007/s00526-009-0271-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M and N be compact Riemannian manifolds. To prove the global existence and convergence of the heat flow for harmonic maps between M and N, it suffices to show the nonexistence of harmonic spheres and nonexistence of quasi-harmonic spheres. In this paper, we prove that, if the universal covering of N admits a nonnegative strictly convex function with polynomial growth, then there are no quasi-harmonic spheres nor harmonic spheres. This generalizes the famous Eells-Sampson's theorem (Am J Math 86:109-169, [7]).

引用

页码：441 / 460

页数：20

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