Volume growth and the topology of manifolds with nonnegative Ricci curvature.

Title: Volume growth and the topology of manifolds with nonnegative Ricci curvature.
Identifier: AAI3310602
identifier: 3310602
Creator: Munn, Michael.
Contributor: Adviser: Christina Sormani
Date: 2008
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: Let Mn be a complete, open Riemannian manifold with Ric ≥ 0. In 1994, Grigori Perelman showed that there exists a constant deltan > 0, depending only on the dimension of the manifold, such that if the volume growth satisfies alpha M := limr→infinity VolBpr wnrn , then Mn is contractible. Here we employ the techniques of Perelman to find specific lower bounds for the volume growth, alpha(k,n), depending only on k and n, which guarantee the individual k-homotopy group of Mn is trivial.;In addition, we extend these results to the setting of metric measure spaces Y which can be realized as the pointed metric measure limit of a sequence {lcub} Mni,pi {rcub} of complete, open connected Riemannian manifolds with Ric RicMi ≥ 0, provided the limit space Y satisfies the same lower bounds on volume growth, i.e. alphaY > alpha(k,n).
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.

Media: Volume growth and the topology of manifolds with nonnegative Ricci curvature.