WebNov 27, 1998 · Lorentzian versions of classical Riemannian volume comparison theorems by Gunther, Bishop and Bishop-Gromov, are stated for suitable natural subsets of general semi-Riemannian manifolds. The problem is more subtle in the Bishop-Gromov case, which is extensively discussed. For the general semi-Riemannian case, a local version of the … WebSep 9, 2015 · For example, Bishop-Gromov volume comparison immediately implies that the volume growth of any complete open manifold of nonnegative Ricci curvature has is …

The Comparison Geometry of Ricci Curvature

WebProblems in Comparison Geometry In all problems below, (M;g) is a complete smooth Riemannian manifold, and Sn k denotes the n-dimensional round sphere of radius p1 k, which is simply denoted Snif k= 1. Problems related to Bishop-Gromov relative volume comparison 1. Cheng’s Theorem (Rigidity in Bonnet-Myers). If (Mn;g) has Ric (n 1)k>0 … WebVolume Comparison Theorem • Let (M,g) be a complete Riemannian manifold, and Bp(r) be a ball which does not meet Cut(p). — Instead of working with A, we work with B =: … fitech 30012 review

(PDF) Bishop and Laplacian comparison theorems on

Webponogov. More recently, comparison theorems in terms of the Ricci cur-vature such as the Bishop{Gromov volume comparison theorem have played an important role leading to such results as the Chen maximal diameter theorem, see the wonderful survey article by Karcher [23]. In Lorentzian geometry and semi-Riemannian geometry, on the other WebAbstract. In this paper, we generalize the Cheng's maximal diameter theorem and Bishop volume comparison theorem to the manifold with the Bakry-Emery Ricci curvature. As their applications, we obtain some rigidity theorems on the warped product. WebOct 13, 2024 · Download PDF Abstract: We give several Bishop-Gromov relative volume comparisons with integral Ricci curvature which improve the results in \cite{PW1}. Using … can handbrake download youtube videos