Geodesic
Calabi flow, geodesic rays, and uniqueness of constant scalar curvature Kähler metrics
Xiuxiong Chen1 ; Song Sun2
1Stony Brook University, Stony Brook, NY and<br/>School of Mathematics, University of Science and Technology of China, Hefei, Anhui, China
2Department of Mathematics and Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY
Annals of mathematics, Tome 180 (2014) no. 2, pp. 407-454
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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.

DOI : 10.4007/annals.2014.180.2.1

Xiuxiong Chen  1   ; Song Sun  2

1 Stony Brook University, Stony Brook, NY and<br/>School of Mathematics, University of Science and Technology of China, Hefei, Anhui, China
2 Department of Mathematics and Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY 
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     title = {Calabi flow, geodesic rays, and uniqueness of constant scalar curvature {K\"ahler} metrics},
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     pages = {407--454},
     year = {2014},
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Xiuxiong Chen; Song Sun. Calabi flow, geodesic rays, and uniqueness of constant scalar curvature Kähler metrics. Annals of mathematics, Tome 180 (2014) no. 2, pp. 407-454. doi: 10.4007/annals.2014.180.2.1

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