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]).
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页码：441 / 460
页数：20
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