Existence of Weak Conical Kähler-Einstein Metrics Along Smooth Hypersurfaces

Abstract

The existence of \emph{weak conical Kähler-Einstein} metrics along smooth hypersurfaces with angle between $0$ and $2\pi$ is obtained by studying a smooth continuity method and a \emph{local Moser's iteration} technique. In the case of negative and zero Ricci curvature, the $C^0$ estimate is unobstructed; while in the case of positive Ricci curvature, the $C^0$ estimate obstructed by the properness of the \emph{twisted K-Energy}. As soon as the $C^0$ estimate is achieved, the local Moser iteration could improve the \emph{rough bound} on the approximations to a \emph{uniform $C^2$ bound}, thus produce a \emph{weak conical Kähler-Einstein} metric. The method used here do not depend on the bound of any background conical Kähler metrics.

15 pages

References in corpus (3)

• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• Conical Kahler-Einstein metric revisited
• Ricci flat Kahler metrics with edge singularities

Cited by in corpus (5)

• Smooth approximations of the Conical Kahler-Ricci flows
• On the long time behaviour of the Conical Kähler- Ricci flows
• On the regularity problem of complex Monge-Ampere equations with conical singularities
• On the boundary behavior of Kähler-Einstein metrics on log canonical pairs
• $C^{2,\alpha }$-estimate for Monge-Ampere equations with Hölder-continuous right hand side