Einstein Manifolds and Extremal Kahler Metrics

TL;DR

This paper introduces new existence theorems for extremal Kähler metrics and provides a novel proof that CP2#2(-CP2) admits an Einstein metric, using deformation and bubbling techniques.

Contribution

It offers a new proof for the existence of Einstein metrics on CP2#2(-CP2) and establishes novel existence results for extremal Kähler metrics.

Findings

CP2#2(-CP2) admits an Einstein metric

New existence theorems for extremal Kähler metrics

Deformation method leading to Einstein metric existence

Abstract

In joint work with Chen and Weber, the author has elsewhere shown that CP2#2(-CP2) admits an Einstein metric. The present paper gives a new and rather different proof of this fact. Our results include new existence theorems for extremal Kahler metrics, and these allow one to prove the above existence statement by deforming the Kahler-Einstein metric on CP2#3(-CP2) until bubbling-off occurs.