Volume growth, curvature decay, and critical metrics

Gang Tian, Jeff Viaclovsky

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

We make some improvements to our previous results in [TV05a] and [TV05b], First, we prove a version of our volume growth theorem which does not require any assumption on the first Betti number. Second, we show that our local regularity theorem only requires a lower volume growth assumption, not a full Sobolev constant bound. As an application of these results, we can weaken the assumptions of several of our theorems in [TV05a] and [TV05b].

Original languageEnglish (US)
Pages (from-to)889-911
Number of pages23
JournalCommentarii Mathematici Helvetici
Volume83
Issue number4
DOIs
StatePublished - Jan 1 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • 58E11
  • Primary 53c21
  • Secondary 58d27

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