28 research outputs found
Applications of Some Elliptic Equations in Riemannian Manifolds
Let be a compact Riemannian manifold with smooth boundary B
and nonnegative Bakry-Emery Ricci curvature. In this paper, we use the
solvability of some elliptic equations to prove some estimates of the weighted
mean curvature and some related rigidity theorems. As their applications, we
obtain some lower bound estimate of the first nonzero eigenvalue of the
drifting Laplacian acting on functions on B and some corresponding rigidity
theorems
Non-ancient solution of the Ricci flow
For any complete noncompact Khler manifold with nonnegative and
bounded holomorphic bisectional curvature,we provide the necessary and
sufficient condition for non-ancient solution to the Ricci flow in this paper.Comment: seven pages, latex fil