Journal of Differential Geometry

Bernstein theorem and regularity for a class of Monge-Ampère equations

Huaiyu Jian and Xu-Jia Wang

Full-text: Open access

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.

Article information

Source
J. Differential Geom., Volume 93, Number 3 (2013), 431-469.

Dates
First available in Project Euclid: 26 February 2013

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1361844941

Digital Object Identifier
doi:10.4310/jdg/1361844941

Mathematical Reviews number (MathSciNet)
MR3024302

Zentralblatt MATH identifier
1278.35120

Citation

Jian, Huaiyu; Wang, Xu-Jia. Bernstein theorem and regularity for a class of Monge-Ampère equations. J. Differential Geom. 93 (2013), no. 3, 431--469. doi:10.4310/jdg/1361844941. https://projecteuclid.org/euclid.jdg/1361844941


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