On the asymptotic geometry of nonpositively curved manifolds
type: Item
instance of: scholarly article
title: On the asymptotic geometry of nonpositively curved manifolds
zbMATH Open document ID: 0896.53033
published in: Geometric and Functional Analysis. GAFA
publication date: 1998-10-06T00:00:00Z
review text: Let \(M\) be a non-flat complete simply connected manifold with \(K_M\leq 0\). Suppose that \(M\) admits a cocompact discrete group of isometries. For \(p\in M\), denote by \(s(r,p)\) the volume of the geodesic sphere of radius \(r\) about \(p\). The main result of the paper is \[ s(r,p)\approx r^{{k- 1\over 2}}\cdot e^{hr}, \] where \(k\) is the geometric rank and \(h\) is the volume entropy of \(M\).
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
zbMATH DE Number: 1123733
zbMATH Keywords: nonpositively curved manifolds
zbMATH Keywords: geodesic flow
zbMATH Keywords: volume entropy
zbMATH Keywords: asymptotic volume
zbMATH Keywords: volume growth
author: Gerhard Knieper
reviewed by: Werner Ballmann
MaRDI profile type: Publication
full work available at URL: s000390050025
OpenAlex ID: W2006977414
DOI: 10.1007/S000390050025
description: scientific article; zbMATH DE number 1123733