Volume growth, curvature decay, and critical metrics

Abstract

We make some improvements to our previous results. 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. These results allow us to weaken the assumptions of our previous volume growth and convergence theorems.

19 pages

Cited by in corpus (1)

• Moduli spaces of critical Riemannian metrics with L^{n/2} norm curvature bounds