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Extremal metrics on toric surfaces:a continuity method

S.K. Donaldson Imperial College, Queen’s Gate

Differential Geometry mathscidoc:1609.10073

Journal of Differential Geometry, 79, (3), 389-432, 2008
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.
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@inproceedings{s.k.2008extremal,
  title={EXTREMAL METRICS ON TORIC SURFACES:A CONTINUITY METHOD},
  author={S.K. Donaldson},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909132808008723730},
  booktitle={Journal of Differential Geometry},
  volume={79},
  number={3},
  pages={389-432},
  year={2008},
}
S.K. Donaldson. EXTREMAL METRICS ON TORIC SURFACES:A CONTINUITY METHOD. 2008. Vol. 79. In Journal of Differential Geometry. pp.389-432. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909132808008723730.
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