A weighted gradient estimate for solutions of $ L^p $ Christoffel-Minkowski problem

Abstract

We extend the weighted gradient estimate for solutions of nonlinear PDE associated to the prescribed $ k $-th $ L^p $-area measure problem to the case $ 0 < p < 1 $. The estimate yields non-collapsing estimate for symmetric convex bodied with prescribed $ L^p $-area measures.

Keywords

• area measures
• christoffel-minkowski problem
• constant rank theorem