黎曼多面体与调和映射的Liouville型定理
Riemannian Polyhedra and Liouville-type Theorems for Harmonic maps
摘要：
本文研究了从黎曼多面体到Alexandrov意义下的（局部）非正曲测地空间的调和映射。在两种不同的源空间假设下，证明了下调和函数和调和映射的Liouville型定理。首先证明了Schoen-Yau定理在具有非负里奇曲率的完备（光滑）伪流形上的类似定理。然后研究了2-抛物型容许黎曼多面体，证明了关于它们的几个消失结果。
英文摘要：
This paper is a study of harmonic maps from Riemannian polyhedra to (locally) non-positively curved geodesic spaces in the sense of Alexandrov. We prove Liouville-type theorems for subharmonic functions and harmonic maps under two different assumptions on the source space. First we prove the analogue of the Schoen-Yau Theorem on a complete (smooth) pseudomanifolds with non-negative Ricci curvature. Then we study 2-parabolic admissible Riemannian polyhedra and prove some vanishing results on them.
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