ﻻ يوجد ملخص باللغة العربية
We give several Bishop-Gromov relative volume comparisons with integral Ricci curvature which improve the results in cite{PW1}. Using one of these volume comparisons, we derive an estimate for the volume entropy in terms of integral Ricci curvature which substantially improves an earlier estimate in cite{Au2} and give an application on the algebraic entropy of its fundamental group. We also extend the almost minimal volume rigidity of cite{BBCG} to integral Ricci curvature.
We will show the Cheeger-Colding segment inequality for manifolds with integral Ricci curvature bound. By using this segment inequality, the almost rigidity structure results for integral Ricci curvature will be derived by a similar method as in cite
Let $M^n$ be a complete, open Riemannian manifold with $Ric geq 0$. In 1994, Grigori Perelman showed that there exists a constant $delta_{n}>0$, depending only on the dimension of the manifold, such that if the volume growth satisfies $alpha_M := lim
We are concerned with the study of different notions of curvature on graphs. We show that if a graph has stronger inner-outer curvature growth than a model graph, then it has faster volume growth too. We also study the relationhips of volume growth w
For Riemannian manifolds with a smooth measure $(M, g, e^{-f}dv_{g})$, we prove a generalized Myers compactness theorem when Bakry--Emery Ricci tensor is bounded from below and $f$ is bounded.
In this paper we prove new classification results for nonnegatively curved gradient expanding and steady Ricci solitons in dimension three and above, under suitable integral assumptions on the scalar curvature of the underlying Riemannian manifold. I