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

The Journal of Geometric Analysis volume 31, pages1471–1509(2021)Cite this article

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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Author information

Affiliations

  1. School of Mathematical Sciences and BICMR, Peking University, Yiheyuan Road 5, Beijing, 100871, People’s Republic of China

    Gang Tian

  2. School of Mathematical Sciences, Zhejiang University, Zheda Road 38, Hangzhou, 310027, Zhejiang, People’s Republic of China

    Feng Wang

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  1. Gang Tian
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  2. Feng Wang
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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