A formal Riemannian structure on conformal classes and the inverse Gauss curvature flow
Abstract: We define a formal Riemannian metric on a given conformal class of metrics with signed curvature on a closed Riemann surface. As it turns out this metric is the well-known Mabuchi-Semmes-Donaldson metric of Kähler geometry in a different guise. The metric has many interesting properties, and in particular we show that the classical Liouville energy is geodesically convex. This suggests a different approach to the uniformization theorem by studying the negative gradient flow of the normalized Liouville energy with respect to this metric, a new geometric flow whose principal term is the inverse of the Gauss curvature. We prove long time existence of solutions with arbitrary initial data and weak convergence to constant scalar curvature metrics by exploiting the metric space structure.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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A formal Riemannian structure on conformal classes and the inverse Gauss curvature flow ; volume:4 ; number:1 ; year:2019 ; pages:30-50 ; extent:21
Geometric flows ; 4, Heft 1 (2019), 30-50 (gesamt 21)
- Creator
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Gursky, Matthew J.
Streets, Jeffrey
- DOI
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10.1515/geofl-2019-0003
- URN
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urn:nbn:de:101:1-2501051745308.674598775629
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:30 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Gursky, Matthew J.
- Streets, Jeffrey
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