Strictly Locally Convex Radial Graphs of Prescribed Curvature and Boundary in Space Forms

Abstract

We obtain $C^2$ a priori estimates for solutions of the nonlinear second-order elliptic equation related to the geometric problem of finding a strictly locally convex hypersurface with prescribed curvature and boundary in a space form. Under the assumption of a strictly locally convex subsolution, we establish existence results by using degree theory arguments.

Add existence results in $S_{+}^{n+1}$. arXiv admin note: text overlap with arXiv:1805.08107