Kähler–Einstein metrics with edge singularities


This article considers the existence and regularity of Kähler–Einstein metrics on a compact Kähler 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 $2\pi \beta \leq 2\pi$. 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 $2\pi \beta < 2\pi$.


Thalia Jeffres

Wichita State University, Wichita, KS

Rafe Mazzeo

Stanford University, Stanford, CA

Yanir A. Rubinstein

University of Maryland, College Park, MD