Calabi flow, geodesic rays, and uniqueness of constant scalar curvature Kähler metrics

Xiuxiong Chen; Song Sun

doi:https://doi.org/10.4007/annals.2014.180.2.1

Pages 407-454 from Volume 180 (2014), Issue 2 by Xiuxiong Chen, Song Sun

Abstract

We prove that constant scalar curvature Kähler metric “adjacent” to a fixed Kähler class is unique up to isomorphism. The proof is based on the study of a fourth order evolution equation, namely, the Calabi flow, from a new geometric perspective, and on the geometry of the space of Kähler metrics.

Milestones

Received: 12 April 2010
Revised: 22 June 2013
Accepted: 4 November 2013
Published online: 1 September 2014

Authors

Xiuxiong Chen

Stony Brook University, Stony Brook, NY and
School of Mathematics, University of Science and Technology of China, Hefei, Anhui, China

Song Sun

Department of Mathematics and Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY