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arXiv · 1105.5216

Kahler-Einstein metrics with edge singularities

T. Jeffres·Rafe Mazzeo·Yanir A. Rubinstein
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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 $2πβ$ along a smooth divisor $D$. We prove existence of such metrics with negative, zero and some positive cases for all cone angles $2πβ\leq 2π$. 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 $2πβ< 2π$.

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T. Jeffres, Rafe Mazzeo, Yanir A. Rubinstein. 2015-08-08. Kahler-Einstein metrics with edge singularities. https://doi.org/10.4007/annals.2016.183.1.3

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