On interior regularity and Liouville's theorem for harmonic mappings
On interior regularity and Liouville's theorem for harmonic mappings
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关于调和映射的内部正则性和刘维尔定理
DOI：
10.1007/bf01171743
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发表时间：
1983
影响因子：
0.6
通讯作者：
A. Tachikawa
中科院分区：
文献类型：
--
作者：
A. Tachikawa
众所周知，弱调和映射U∶M→N（M，N：黎曼流形）是正则的，如果像U（M）包含在某个充分小球中，并且在这种情况下Liouville定理成立.本文证明了如果U极小化能量泛函且目标流形N的截面曲率由到N的某个不动点的距离的适当函数所限定，则U（M）的小性条件可以解除.
It is well known that the weakly harmonic mapping U∶M→N (M,N: Riemannian manifolds) is regular if the image U(M) is contained in some sufficiently small ball and for this case Liouville's theorem is valid. In this paper we show that the smallness condition for U(M) can be released if U minimizes the energy functional and the sectional curvatures of the target manifold N are bounded by some suitable function of the distance from some fixed point of N.