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

2018/06/19 by Sui, Zhenan
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.07205

Abstract

We obtain C² 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.

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