Volume growth, curvature decay, and critical metrics

Details Volume growth, curvature decay, and critical metrics Volume growth, curvature decay, and critical metrics

2006-12-17

arxiv.org/abs/math/0612491v1

Final version: Comm. Math. Helv. 83, Issue 4, 2008, pages 889-911

Mathematics

Differential Geometry

19 pages

Scientific paper

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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