The slitting and vanishing theorems on complete manifolds
Abstract:
It is well-known that there are interesting relationships between geometry,
topology and the function theory on Riemannian and K\"{a}hler manifolds. For
example, Li and Wang proved splitting and vanishing theorems on complete
manifolds whose Ricci curvature is bounded from below in term of bottom of
spectrum. Consequently, they obtained topology and geometric structure of
such these manifolds. Their theory generalized the work of Witten-Yau, Cai-
Galloway and X. D. Wang. In this talk, I will do the further extention of
the above results. I will show several splitting and vanishing theorems on
Riemannian, K\"{a}hler manifolds, and smooth metric measure spaces. Some
examples and applications are also given.
Tea Time: 3:30PM R707(七樓休息室)