Rui-Feng Xu

Positive Weighted Curvatures on Compact Manifolds with Weighted Convex Boundary and Proper Manifolds

Given a Riemannian manifold $(M,g)$ equipped with a positive density function $f = e^{-\varphi}$, we study the weighted sectional curvature $\overline{\sec}_\varphi(U,V)$ and the $k$-th intermediate weighted Ricci curvature $\overline{\text{Ric}}_{k,\varphi}(U,V)$. We show that $\overline{\sec}_\varphi(U,V)$ and $\over...