Rigidity Theorems for Diameter Estimates of Compact Manifold with Boundary
Rigidity Theorems for Diameter Estimates of Compact Manifold with Boundary
Let $(N,g)$ be an $n$-dimensional complete Riemannian manifold with nonempty boundary $\pt N$. Assume that the Ricci curvature of $N$ has a negative lower bound $Ric\geq -(n-1)c^2$ for some $c>0$, and the mean curvature of the boundary $\pt N$ satisfies $H\geq (n-1)c_0>(n-1)c$ for some $c_0>c>0$. Then a known result (see …