Liouville theorems for self-similar solutions of heat flows

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	Liouville theorems for self-similar solutions of heat flows
	Li, Jiayu1,2 ; Wang, Meng 3
	2009
发表期刊	JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
ISSN	1435-9855
卷号	11 期号:1 页码:207-221
摘要	Let N be a compact Riemannian manifold. A quasi-harmonic sphere on N is a harmonic maps from (R(m), e(-vertical bar x vertical bar 2/2(m-2))ds(0)(2)) to N (m >= 3) with finite energy ([LnW]). Here ds(0)(2) is the Euclidean metric in R(m). Such maps arise from the blow-up analysis of the heat flow at a singular point. In this paper, we prove some kinds of Liouville theorems for the quasi-harmonic spheres. It is clear that the Liouville theorems imply the existence of the heat flow to the target N. We also derive gradient estimates and Liouville theorems for positive quasi-harmonic functions.
关键词	Harmonic sphere self-similar solution quasi-harmonic sphere heat flow
语种	英语
资助项目	NSFC[10701064]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000263562800005
出版者	EUROPEAN MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8598
专题	数学所
通讯作者	Li, Jiayu
作者单位	1.Abdus Salam Int Ctr Theoret Phys, I-34100 Trieste, Italy 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 3.Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China
推荐引用方式 GB/T 7714	Li, Jiayu,Wang, Meng. Liouville theorems for self-similar solutions of heat flows[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY,2009,11(1):207-221.
APA	Li, Jiayu,&Wang, Meng.(2009).Liouville theorems for self-similar solutions of heat flows.JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY,11(1),207-221.
MLA	Li, Jiayu,et al."Liouville theorems for self-similar solutions of heat flows".JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY 11.1(2009):207-221.