The Dirichlet problem for prescribed curvature equations of $p$-convex hypersurfaces

TL;DR

This paper addresses the Dirichlet problem for p-convex hypersurfaces with prescribed curvature, establishing existence and interior curvature estimates for solutions under homogeneous boundary conditions.

Contribution

It proves the existence of solutions to the prescribed curvature equation for p-convex hypersurfaces and provides interior curvature estimates.

Findings

Existence of a graphic hypersurface satisfying the prescribed curvature equation.

Interior curvature estimates for solutions.

Solutions adhere to homogeneous boundary conditions.

Abstract

In this paper, we study the Dirichlet problem for $p$-convex hypersurfaces with prescribed curvature. We prove that there exists a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition. An interior curvature estimate is also obtained.