Kahler-Einstein metrics with edge singularities

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 $2\pi \beta \le 2\pi$. 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 $2\pi \beta <2\pi$.

with an appendix by Chi Li and Yanir A. Rubinstein. Accepted by Annals of Math

References in corpus (1)

• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, I

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