2011/04/04 by An-Min Li, Li, An-Min, Ruiwei Xu +5
Mathematics · #35J60 #53A15 #58J60 #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1104.0450
openalex publication_date 2011/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.