Abstract.
The main result of the paper is an existence theorem for a constant scalar curvature Kahler metric on a toric surface, assuming the K-stability of the manifold. The proof builds on earlier papers by the author, which reduce the problem to certain a priori estimates. These estimates are obtained using a combination of arguments from Riemannian geometry and convex analysis. The last part of the paper contains a discussion of the phenomena that can be expected when the K-stability does not hold and solutions do not exist.
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Received: May 2008, Revision: December 2008, Accepted: December 2008
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Donaldson, S.K. Constant Scalar Curvature Metrics on Toric Surfaces. Geom. Funct. Anal. 19, 83–136 (2009). https://doi.org/10.1007/s00039-009-0714-y
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DOI: https://doi.org/10.1007/s00039-009-0714-y