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We discuss the optimal regularity of solutions to degenerate elliptic and parabolic fully nonlinear partial differential equations, in particular the evolution of a hypersurface M n t in R n+1 by powers of its Gaussian curvature and other nonlinear functions of its principal curvatures. We will also discuss the regularity question related to the Weyl problem with nonnegative curvature, which involves a fully-nonlinear degenerate elliptic equation of Monge-Ampère type.doi:10.4310/sdg.2014.v19.n1.a4 fatcat:6gxq2lnaxrdn5oyv4vlkikesvy