Kahler-Einstein metrics with edge singularities

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Authors
Jeffres, Thalia D.
Mazzeo, Rafe
Rubinstein, Yanir A.
Issue Date
2016-01
Type
Article
Language
en_US
Keywords
Degenerate complex Monge , Ampère equation , Edge operators , Kähler Einstein metrics , Research Subject Categories::MATHEMATICS
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Abstract

This article considers the existence and regularity of Kahler Einstein metrics on a compact Kahler manifold M with edge singularities with cone angle 2 pi beta along a smooth divisor D. We prove existence of such metrics with negative, zero and some positive cases for all cone angles 2 pi beta <= 2 pi. The results in the positive case parallel those in the smooth case. We also establish that solutions of this problem are polyhomogeneous, i.e., have a complete asymptotic expansion with smooth coefficients along D for all 2 pi beta < 2 pi.

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Jeffres, Thalia D.; Mazzeo, Rafe; Rubinstein, Yanir A. 2016. Kahler-Einstein metrics with edge singularities. Annals of Mathematics, vol. 183:no. 1:pp 95-176
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Princeton University
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0003-486X
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