Kahler-Einstein metrics with edge singularities

Understand

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 $2\pi\beta\leq 2\pi$.
• 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 $2\pi\beta < 2\pi$.