Volume growth, curvature decay, and critical metrics

  • Gang Tian

    Princeton University, USA
  • Jeff A. Viaclovsky

    University of Wisconsin, Madison, United States


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].

Cite this article

Gang Tian, Jeff A. Viaclovsky, Volume growth, curvature decay, and critical metrics. Comment. Math. Helv. 83 (2008), no. 4, pp. 889–911

DOI 10.4171/CMH/147