Smooth approximation of conic K\"ahler metric with lower Ricci curvature bound

TL;DR

This paper demonstrates that conic Kähler metrics with a lower Ricci curvature bound can be approximated by smooth metrics with the same curvature bound, even with singularities along normal crossing divisors, extending Tian's method.

Contribution

It introduces a method to approximate conic Kähler metrics with lower Ricci bounds by smooth metrics, including cases with normal crossing divisors.

Findings

Conic Kähler metrics can be approximated smoothly while preserving Ricci curvature bounds.

The approximation applies to metrics with singularities along simple normal crossing divisors.

The method extends Tian's approach to more general conic settings.

Abstract

We apply Tian's method in Kahler-Einstein problem to prove that a conic K\''ahler metric with lower Ricci curvature bound can be approximated by smooth K\''ahler metrics with the same lower Ricci curvature bound. Furthermore, conic singularities here can be along a simple normal crossing divisor.