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

Xiuxiong Chen; Song Sun

doi:10.4007/annals.2014.180.2.1

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

Xiuxiong Chen
, Song Sun

Mathematics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	407-454
Number of pages	48
Journal	Annals of Mathematics
Volume	180
Issue number	2
DOIs	https://doi.org/10.4007/annals.2014.180.2.1
State	Published - 2014

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10.4007/annals.2014.180.2.1

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abstract = "We prove that constant scalar curvature K{\"a}hler metric \textbackslash{}adjacent{"} to a xed K{\"a}hler class is unique up to isomorphism. The proof is based on the study of a fourth order evolution equation, namely, the Calabi ow, from a new geometric perspective, and on the geometry of the space of K{\"a}hler metrics.",

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AB - We prove that constant scalar curvature Kähler metric \adjacent" to a xed Kähler class is unique up to isomorphism. The proof is based on the study of a fourth order evolution equation, namely, the Calabi ow, from a new geometric perspective, and on the geometry of the space of Kähler metrics.

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DO - 10.4007/annals.2014.180.2.1

M3 - Article

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VL - 180

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JO - Annals of Mathematics

JF - Annals of Mathematics

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

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