Sheng, WeiminTrudinger, NeilWang, Xu-Jia2015-12-070025-5874http://hdl.handle.net/1885/27400In this paper we study the regularity of closed, convex surfaces which achieve maximal affine area among all the closed, convex surfaces enclosed in a given domain in the Euclidean 3-space. We prove the C1,α regularity for general domains and C1,1 regula200610.1007/s00209-005-0862-12015-12-07