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Volume growth, curvature decay, and critical metrics

Jeff Viaclovsky·Gang Tian
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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.

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Jeff Viaclovsky, Gang Tian. 2006-12-17. Volume growth, curvature decay, and critical metrics. https://arxiv.org/abs/math/0612491

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