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

Weisong Dong

Published 2021-07-28, updated 2022-04-28Version 2

In this paper, we establish the curvature estimates for $p$-convex hypersurfaces in $\mathbb{R}^{n+1}$ of prescribed curvature with $p\geq \frac{n}{2}$. 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.