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Results in Mathematics

, 56:109 | Cite as

A Bernstein Property of Some Fourth Order Partial Differential Equations

  • An-Min LiEmail author
  • Fang Jia
Article

Abstract.

In this paper we prove a Bernstein property of solutions for a class of nonlinear, fourth order partial differential equations, including the affine maximal surface equation and the Abreu equation. As a corollary we give a new analytic proof for Chern’s Affine Bernstein Conjecture.

Mathematics Subject Classification (2000).

53A15 35J60 35J65 53C20 53C21 53C24 53C40 58J60 

Keywords.

Bernstein property affine Bernstein problems nonlinear PDEs of fourth order relative hypersurfaces Calabi metric characterization of quadrics 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of MathematicsSichuan UniversityChengdu, SichuanP.R. China

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