Hypersurfaces of prescribed curvature measure

2012/06/27 by Pengfei Guan, Junfang Li, YanYan Li · 3 citations
Mathematics · #Point processes and geometric inequalities #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · doi:10.1215/00127094-1645550

Abstract

We consider the corresponding Christoffel–Minkowski problem for curvature measures. The existence of star-shaped (n−k)-convex bodies with prescribed kth curvature measures (k>0) has been a longstanding problem. This is settled in this paper through the establishment of a crucial a priori C2-estimate for the corresponding curvature equation on Sn.

Citations

• The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian

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