Comparison theorems for the volume of a geodesic ball with a product of space forms as a model
type: Item
instance of: scholarly article
title: Comparison theorems for the volume of a geodesic ball with a product of space forms as a model
zbMATH Open document ID: 0836.53026
DOI: 10.1007/BF01222855
author: Ana Lluch
author: Vicente Miquel
published in: Journal of Geometry
publication date: 1996-02-01T00:00:00Z
review text: The classical theorem of Bishop and Günter gives a comparison between the volume of a geodesic ball of radius \(r\) in a Riemannian manifold of dimension \(n\) with Ricci curvature \(\rho\) bounded from below by some constant \((n- 1)k\) and the volume of a geodesic ball of radius \(r\) in a space form of sectional curvature \(k\). The authors prove two comparison theorems for the volume of a geodesic ball in a Riemannian manifold taking as a model a geodesic ball in the product of two space forms.
reviewed by: Andrew Bucki
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 827392
zbMATH Keywords: bounded Ricci curvature
zbMATH Keywords: volume of a geodesic ball
zbMATH Keywords: comparison theorems
MaRDI profile type: Publication
cites work: Q5341449
cites work: Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
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cites work: Product tube formulas
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full work available at URL: https://doi.org/10.1007/bf01222855
OpenAlex ID: W2082769104
description: scientific article; zbMATH DE number 827392