Volume growth, curvature decay, and critical metrics

• Autores: Gang Tian, Jeff Viaclovsky
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 83, Nº 4, 2008, págs. 889-911
• Idioma: inglés
• DOI: 10.4171/cmh/147
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• Resumen

  • 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].