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Kähler–Einstein metrics: From cones to cusps

  • Henri Guenancia ORCID logo
Veröffentlicht/Copyright: 3. Mai 2018

Abstract

In this note, we prove that on a compact Kähler manifold X carrying a smooth divisor D such that KX+D is ample, the Kähler–Einstein cusp metric is the limit (in a strong sense) of the Kähler–Einstein conic metrics when the cone angle goes to 0. We further investigate the boundary behavior of those and prove that the rescaled metrics converge to a cylindrical metric on *×n-1.

Award Identifier / Grant number: DMS-1510214

Funding statement: The author is partially supported by NSF Grant DMS-1510214.

Acknowledgements

I am grateful to Vincent Guedj who suggested this problem to me. Also, I would like to thank Song Sun for very insightful discussions about this paper.

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Received: 2015-06-21
Revised: 2017-12-21
Published Online: 2018-05-03
Published in Print: 2020-02-01

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