Prescription of Gauss curvature on compact hyperbolic orbifolds

Jérôme Bertrand

doi:10.3934/dcds.2014.34.1269

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2014, Volume 34, Issue 4: 1269-1284. Doi: 10.3934/dcds.2014.34.1269

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Prescription of Gauss curvature on compact hyperbolic orbifolds

Jérôme Bertrand^1,

1.
Institut de Mathématiques de Toulouse, UMR CNRS 5219, Université Toulouse III, 31062 Toulouse cedex 9

Received: September 30, 2012

Revised: February 28, 2013

Published: March 2014

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Abstract

In this paper, we generalize a result by Alexandrov on the Gauss curvature prescription for Euclidean convex bodies. We prove an analogous result for hyperbolic orbifolds. In addition to the duality theory for convex sets, our main tool comes from optimal mass transport.

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Mathematics Subject Classification: Primary: 49Q20; Secondary: 52C07, 53C42.

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