论文标题
关于Huber的类型定理一般维度
On Huber's type theorems in general dimensions
论文作者
论文摘要
在本文中，我们介绍了Huber \ cite {Hu57}的著名有限点形式的相结合定理的一些扩展，以完全开放表面，以基于相结合几何形状的N-Laplace方程。如果可以将最小的RICCI曲率曲率的负部分赋予完整的共形度量，那么我们能够得出结论圆形球体中的一个域必须是有限的多个点。我们的证明是基于在我们较早的工作\ cite {mq18}中对n-superharmonic函数的Arsove-Huber类型定理的加强版本。此外，使用p-降解性，我们将Schoen-yau的注射率定理允许一些负曲率，因此建立了有限的点共形性压实定理，以使折射物中的歧管浸入圆形球体中。作为副产品，我们仅凭N-核心就建立了保形浸入式的注入性，这本身就在保形几何形状中很有趣。
In this paper we present some extensions of the celebrated finite point conformal compactification theorem of Huber \cite{Hu57} for complete open surfaces to general dimensions based on the n-Laplace equations in conformal geometry. We are able to conclude a domain in the round sphere has to be the sphere deleted finitely many points if it can be endowed with a complete conformal metric with the negative part of the smallest Ricci curvature satisfying some integrable conditions. Our proof is based on the strengthened version of the Arsove-Huber's type theorem on n-superharmonic functions in our earlier work \cite{MQ18}. Moreover, using p-parabolicity, we push the injectivity theorem of Schoen-Yau to allow some negative curvature and therefore establish the finite point conformal compactification theorem for manifolds that have a conformal immersion into the round sphere. As a side product we establish the injectivity of conformal immersions from n-parabolicity alone, which is interesting by itself in conformal geometry.
