A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications

A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications

We extend the classical Bishop-Gromov volume comparison from constant Ricci curvature lower bound to radially symmetric Ricci curvature lower bound, and apply it to investigate the volume growth, total Betti number, and finite topological type of manifolds with nonasymptotically almost nonnegative R...

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Bibliographic Details
Main Authors: Zisheng Hu, Yadong Jin, Senlin Xu
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2010/758531
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spelling doaj-226c3f2897f54e6dbca225044bf9d8cb2020-11-24T23:58:37ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/758531758531A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its ApplicationsZisheng Hu0Yadong Jin1Senlin Xu2School of Mathematics and Computational Science, Shenzhen University, Shenzhen, Guangdong 518060, ChinaSchool of Mathematics and Physics, Jiangsu Teachers University of Technology, Changzhou, Jiangsu 213001, ChinaDepartment of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, ChinaWe extend the classical Bishop-Gromov volume comparison from constant Ricci curvature lower bound to radially symmetric Ricci curvature lower bound, and apply it to investigate the volume growth, total Betti number, and finite topological type of manifolds with nonasymptotically almost nonnegative Ricci curvature.http://dx.doi.org/10.1155/2010/758531
collection DOAJ
language English
format Article
sources DOAJ
author Zisheng Hu
Yadong Jin
Senlin Xu
spellingShingle Zisheng Hu
Yadong Jin
Senlin Xu
A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications
International Journal of Mathematics and Mathematical Sciences
author_facet Zisheng Hu
Yadong Jin
Senlin Xu
author_sort Zisheng Hu
title A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications
title_short A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications
title_full A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications
title_fullStr A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications
title_full_unstemmed A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications
title_sort volume comparison estimate with radially symmetric ricci curvature lower bound and its applications
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2010-01-01
description We extend the classical Bishop-Gromov volume comparison from constant Ricci curvature lower bound to radially symmetric Ricci curvature lower bound, and apply it to investigate the volume growth, total Betti number, and finite topological type of manifolds with nonasymptotically almost nonnegative Ricci curvature.
url http://dx.doi.org/10.1155/2010/758531
work_keys_str_mv AT zishenghu avolumecomparisonestimatewithradiallysymmetricriccicurvaturelowerboundanditsapplications
AT yadongjin avolumecomparisonestimatewithradiallysymmetricriccicurvaturelowerboundanditsapplications
AT senlinxu avolumecomparisonestimatewithradiallysymmetricriccicurvaturelowerboundanditsapplications
AT zishenghu volumecomparisonestimatewithradiallysymmetricriccicurvaturelowerboundanditsapplications
AT yadongjin volumecomparisonestimatewithradiallysymmetricriccicurvaturelowerboundanditsapplications
AT senlinxu volumecomparisonestimatewithradiallysymmetricriccicurvaturelowerboundanditsapplications
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