Cheeger–Colding–Tian Theory for Conic Kähler–Einstein Metrics

Abstract

In this paper we extend the Cheeger–Colding–Tian theory to the conic Kahler–Einstein metrics. In general, there are no smooth approximations of a family of conic Kahler–Einstein metrics with Ricci curvature uniformly bounded from below. So we have to deal with the technical issues to extend the original arguments.

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Correspondence to Feng Wang.

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Gang Tian: Partially supported by NSFC Grants 11331001. Feng Wang: Partially supported by NSFC Grants 11501501 and the Fundamental Research Funds for the Central Universities 2018QNA3001.

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Tian, G., Wang, F. Cheeger–Colding–Tian Theory for Conic Kähler–Einstein Metrics. J Geom Anal 31, 1471–1509 (2021). https://doi.org/10.1007/s12220-019-00312-1

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Keywords

  • Cheeger–Colding–Tian theory
  • Conic Kahler–Einstein metrics

Mathematics Subject Classification

  • 53C25