从闭流形出发的V-调和映照热流
首发时间:2016-06-08
摘要:本文主要考虑从闭流形出发的V-调和映照。一般来讲,V-调和映照既没有变分结构也没有散度形式,所以调和映照理论发展的许多有用工具不再适用,且这里的分析变得更加困难。因此,当目标流形的截面曲率非正时,本文拟采取Jost-Yau的研究方法,用热流方法证明从紧致黎曼流形出发的V-调和映照的存在性和唯一性。所得到的结果推广了Hermitian调和映照、仿射调和映照和Weyl调和映照的相关定理。
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The heat flow for V-harmonic maps from closed manifolds
Abstract:In this paper, we consider V-harmonic maps from closed manifolds. In general, V-harmonic maps have no variational structure and are not of a divergence form. Therefore many useful tools developed in the theory of harmonic maps are no longer available, and the analysis here is more difficult. Hence when the sectional curvature of the target manifold is nonpositive, by taking similar method of Li-Yau, we obtain the exitence and unqueness of V-harmonic maps from compact Riemannian manifolds by heat flow method. The results we derived generalize the corresponding theorems of Hermitian harmonic maps, affine harmonic maps and Weyl harmonic maps.
Keywords: V-harmonic map existence heat flow
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