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March 2013 Bernstein theorem and regularity for a class of Monge-Ampère equations
Huaiyu Jian, Xu-Jia Wang
J. Differential Geom. 93(3): 431-469 (March 2013). DOI: 10.4310/jdg/1361844941

Abstract

In this paper we first introduce a transform for convex functions and use it to prove a Bernstein theorem for a Monge-Ampère equation in half space.We then prove the optimal global regularity for a class of Monge-Ampère type equations arising in a number of geometric problems such as Poincaré metrics, hyperbolic affine spheres, and Minkowski type problems.

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Huaiyu Jian. Xu-Jia Wang. "Bernstein theorem and regularity for a class of Monge-Ampère equations." J. Differential Geom. 93 (3) 431 - 469, March 2013. https://doi.org/10.4310/jdg/1361844941

Information

Published: March 2013
First available in Project Euclid: 26 February 2013

zbMATH: 1278.35120
MathSciNet: MR3024302
Digital Object Identifier: 10.4310/jdg/1361844941

Rights: Copyright © 2013 Lehigh University

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Vol.93 • No. 3 • March 2013
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