The heat flow and harmonic maps on a class of manifolds

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	The heat flow and harmonic maps on a class of manifolds
	Zhang, X
	1998
发表期刊	PACIFIC JOURNAL OF MATHEMATICS
ISSN	0030-8730
卷号	182 期号:1 页码:157-182
摘要	We study the heat how for harmonic maps from a complete noncompact manifold M which satisfies conditions (a) and (b) in 1. We show that if the target manifold N is complete, the C-2 initial map has bounded image in N and has bounded energy density and bounded tension held, then the short-time solution of (1.1) in 1 exists and is unique. Additional, if the sectional curvature of N is bounded from above, either the long-time solution of (1.1) exists or the energy density of heat flow blows up at a finite time. Moreover, if N has nonpositive sectional curvature and (1.1) has a long-time solution u(.,t) whose energy density increases logarithmically, and there is a point p is an element of M and a sequence t(v) --> infinity such that u(., t(v)) converges uniformly on compact subsets of M to a harmonic map u(infinity) by passing to a subsequence. For this class of manifolds which satisfy (a) and (b), we also get L-p (p > 0) mean-value inequalities for subsolutions of heat equations and gradient estimates for solutions of heat equations.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000072741000009
出版者	PACIFIC JOURNAL MATHEMATICS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13398
专题	数学所
通讯作者	Zhang, X
作者单位	1.Chinese Acad Sci, Morningside Ctr Math, Beijing 100080, Peoples R China 2.Chinese Acad Sci, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhang, X. The heat flow and harmonic maps on a class of manifolds[J]. PACIFIC JOURNAL OF MATHEMATICS,1998,182(1):157-182.
APA	Zhang, X.(1998).The heat flow and harmonic maps on a class of manifolds.PACIFIC JOURNAL OF MATHEMATICS,182(1),157-182.
MLA	Zhang, X."The heat flow and harmonic maps on a class of manifolds".PACIFIC JOURNAL OF MATHEMATICS 182.1(1998):157-182.