Open Access
July 2008 Extremal metrics on toric surfaces: a continuity method
S. K. Donaldson
J. Differential Geom. 79(3): 389-432 (July 2008). DOI: 10.4310/jdg/1213798183

Abstract

The paper develops an existence theory for solutions of the Abreu equation, which include extremal metrics on toric surfaces. The technique employed is a continuity method, combined with “blow-up” arguments. General existence results are obtained, assuming a hypothesis (the “M-condition”) on the solutions, which is shown to be related to the injectivity radius.

Citation

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S. K. Donaldson. "Extremal metrics on toric surfaces: a continuity method." J. Differential Geom. 79 (3) 389 - 432, July 2008. https://doi.org/10.4310/jdg/1213798183

Information

Published: July 2008
First available in Project Euclid: 18 June 2008

MathSciNet: MR2433928
zbMATH: 1151.53030
Digital Object Identifier: 10.4310/jdg/1213798183

Rights: Copyright © 2008 Lehigh University

Vol.79 • No. 3 • July 2008
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