Geometry of Kähler Metrics and Foliations by Holomorphic Discs

Abstract

The purpose of this paper is to establish a completely new partial regularity theory on certain homogeneous complex Monge-Ampere equations. Our partial regularity theory will be obtained by studying foliations by holomorphic curves and and their relations to homogeneous complex Monge-Ampere equations. As applications, we will prove the uniqueness of extremal Kähler metrics and give an necessary condition for existence of extremal Kähler metrics. Further applications will be discussed in our forthcoming papers.

93 pages

References in corpus (1)

• Algebraic and Analytic K-Stability

Cited by in corpus (8)

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• Test configurations and Geodesic rays
• Twisted cscK metrics and Kähler slope stability
• Liouville energy on a topological two sphere
• Note on geodesic rays tamed by simple test configurations
• Canonical metric on a mildly singular Kähler varieties with an intermediate log Kodaira dimension