On the Liouville theorem for harmonic maps
On the Liouville theorem for harmonic maps
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DOI：
10.1090/s0002-9939-1982-0647905-3
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发表时间：
1982
期刊：
影响因子：
--
通讯作者：
H. Choi
中科院分区：
文献类型：
--
作者：
H. Choi
设M和N是完备黎曼流形; M的Ricci曲率下有-A，A > 0，N的截面曲率上有一个正常数K。设u：MN是调和映射，使得u（M）C BR（yo）.如果BR（yo）位于yo的切割轨迹内且R < 7/21 K，则u的能量密度e（u）由仅取决于A、K和R的常数限定。如果A = 0，那么u是一个常数映射。
Suppose M and N are complete Riemannian manifolds; M with Ricci curvature bounded below by -A, A > 0, N with sectional curvature bounded above by a positive constant K. Let u: M N be a harmonic map such that u(M) C BR( yo). If BR(yo) lies inside the cut locus of yo and R < 7/21K, then the energy density e( u) of u is bounded by a constant depending only on A, K and R. If A = 0, then u is a constant map.