Complete submanifolds of manifolds of negative curvature

Abstract

In this article, we give sufficient conditions for a complete non-compact submanifold in a simply connected manifold of negative sectional curvature to have only one end. We also prove some Liouville theorems for harmonic maps from the same kind of submanifolds to manifolds of non-positive curvature.

Vanishing theorems on complete manifolds with weighted Poincaré inequality and applications

“…Based on Theorems 1.1 and 1.3, by using the same arguments as before, we can improve the main results of [6], [24], and [25].…”

Vanishing theorems on complete manifolds with weighted Poincaré inequality and applications

“…Remark 3.13. Based on Theorems 1.1 and 1.3, by using the same arguments as before, we can improve the main results of [6], [24], and [25].…”