Volume growth, curvature decay, and critical metrics

Gang Tian, Jeff Viaclovsky

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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
Issue number4
StatePublished - 2008

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • 58E11
  • Primary 53c21
  • Secondary 58d27


Dive into the research topics of 'Volume growth, curvature decay, and critical metrics'. Together they form a unique fingerprint.

Cite this