Curvature estimates for $p$-convex hypersurfaces of prescribed curvature

Abstract

. In this paper, we establish curvature estimates for p -convex hypersurfaces in R n +1 of prescribed curvature with p ≥ n 2 . The existence of a star-shaped hypersurface of prescribed curvature is obtained. We also prove a type of interior C 2 estimates for solutions to the Dirichlet problem of the corresponding equation. Mathematical Subject Classification (2010): 53C42; 53C21; 35J60.