Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities

TL;DR

This paper introduces methods to approximate Kahler-Einstein metrics with cone singularities on Fano manifolds, laying foundational work for subsequent studies in the series.

Contribution

It provides the first rigorous proof of approximating Kahler-Einstein metrics with cone singularities on Fano manifolds.

Findings

Established approximation techniques for cone singularities

Proved existence of Kahler-Einstein metrics with cone singularities

Laid groundwork for future research in the series

Abstract

This is the first of a series of three papers which provide proofs of results announced recently in arXiv:1210.7494.