




























Let $M$ be a complete Riemannian manifold possibly with a boundary $\partial M$. For any $C^1$-vector field $Z$, by using gradient/functional inequalities of the (reflecting) diffusion process generated by $L:=Δ+Z$, pointwise characterizations are presented for the Bakry-Emery curvature of $L$ and the second fundamental form of $\partial M$ if exists. These extend and strengthen the recent results derived by A. Naber for the uniform norm $\|{\mathbf{Ric}}_Z\|_\infty$ on manifolds without boundary. A key point of the present study is to apply the asymptotic formulas for these two tensors found by the first named author, such that the proofs are significantly simplified.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。