Strictly Locally Convex Hypersurfaces with Prescribed Curvature and Boundary in Space Forms

Abstract

This paper is devoted to $C^2$ a priori estimates for strictly locally convex radial graphs with prescribed Weingarten curvature and boundary in space forms. By constructing two-step continuity process and applying degree theory arguments, existence results in space forms are established for prescribed Gauss curvature equation under the assumption of a strictly locally convex subsolution.