Extremal metrics on toric surfaces: a continuity method
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 sol...
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| Veröffentlicht in: | Journal of differential geometry 2008-07, Vol.79 (3), p.389-432 |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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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| ISSN: | 0022-040X 1945-743X |
| DOI: | 10.4310/jdg/1213798183 |