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Notes on Chern's Affine Bernstein Conjecture

By An-Min Li, Ruiwei Xu, Udo Simon and Fang Jia

Abstract

There were two famous conjectures on complete affine maximal surfaces, one due to E. Calabi, the other to S.S. Chern. Both were solved with different methods about one decade ago by studying the associated Euler-Lagrange equation. Here we survey two proofs of Chern's conjecture in our recent monograph [L-X-S-J], in particular we add some details of the proofs of auxiliary material that were omitted in [L-X-S-J]. We describe the related background in our Introduction. Our survey is suitable as a report about recent developments and techniques in the study of certain Monge-Ampere equations

Topics: Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, 53A15, 35J60, 58J60
Year: 2011
OAI identifier: oai:arXiv.org:1104.0450
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