The Dirichlet problem for harmonic maps from Riemannian polyhedra to spaces of upper bounded curvature
The Dirichlet problem for harmonic maps from Riemannian polyhedra to spaces of upper bounded curvature
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DOI：
10.1090/s0002-9947-04-03498-1
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发表时间：
2005
影响因子：
1.3
通讯作者：
B. Fuglede
中科院分区：
文献类型：
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作者：
B. Fuglede
这是J. Eells和本作者的黎曼多面体之间的剑桥道调和图的延续。具有连续边界数据的调和映射的Dirichlet问题的变分解在边界处是连续的，因此是唯一确定的。区域空间是一个紧致的有边界的可容许黎曼多面体，而目标可以是一个非正亚历山德罗夫曲率的单连通完全测地空间；或者，只要所述映射具有适当的小范围，则目标可以具有上界曲率。本质上，在前一种情况下，进一步证明了调和映射将目标中的凸函数拉回域中的次调和函数。
This is a continuation of the Cambridge Tract Harmonic maps between Riemannian polyhedra, by J. Eells and the present author. The variational solution to the Dirichlet problem for harmonic maps with countinuous boundary data is shown to be continuous up to the boundary, and thereby uniquely determined. The domain space is a compact admissible Riemannian polyhedron with boundary, while the target can be, for example, a simply connected complete geodesic space of nonpositive Alexandrov curvature; alternatively, the target may have upper bounded curvature provided that the maps have a suitably small range. Essentially in the former setting it is further shown that a harmonic map pulls convex functions in the target back to subharmonic functions in the domain.