Uniqueness of extremal Kähler metrics

Xiuxiong Chen, Gang Tian

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

In the infinite dimensional space of Kähler potentials, the geodesic equation of disc type is a complex homogenous Monge-Ampère equation. The partial regularity theory established by Chen and Tian [C. R. Acad. Sci. Paris, Ser. I 340 (5) (2005)] amounts to an improvement of the regularity of the known C1,1 solution to the geodesic of disc type to almost everywhere smooth. For such an almost smooth solution, we prove that the K-energy functional is sub-harmonic along such a solution. We use this to prove the uniqueness of extremal Kähler metrics and to establish a lower bound for the modified K-energy if the underlying Kähler class admits an extremal Kähler metric.

Original languageEnglish (US)
Pages (from-to)287-290
Number of pages4
JournalComptes Rendus Mathematique
Volume340
Issue number4
DOIs
StatePublished - Feb 15 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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