Journal of Differential Geometry

On stability and the convergence of the Kähler-Ricci flow

Duong H. Phong and Jacob Sturm

Abstract

Assuming uniform bounds for the curvature, the exponential convergence of the Kähler-Ricci flow is established under two conditions which are a form of stability: the Mabuchi energy is bounded from below, and the dimension of the space of holomorphic vector fields in an orbit of the diffeomorphism group cannot jump up in the limit.

Article information

Source
J. Differential Geom., Volume 72, Number 1 (2006), 149-168.

Dates
First available in Project Euclid: 28 March 2006

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1143593129

Digital Object Identifier
doi:10.4310/jdg/1143593129

Mathematical Reviews number (MathSciNet)
MR2215459

Zentralblatt MATH identifier
1125.53048

Citation

Phong, Duong H.; Sturm, Jacob. On stability and the convergence of the Kähler-Ricci flow. J. Differential Geom. 72 (2006), no. 1, 149--168. doi:10.4310/jdg/1143593129. https://projecteuclid.org/euclid.jdg/1143593129


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