An expanding curvature flow and the (p,q)-Christoffel-Minkowski problems

2022/03/10 by Chen, Bin, Cui, Jingshi, Zhao, Peibiao
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.05105

Abstract

The present paper introduces a new class of geometric measures, the k-th (p,q)-mixed curvature measures, and a natural correspondence-(p,q)-Christoffel-Minkowski problem is proposed. The (p,q)-Christoffel-Minkowski problem posed here can be regarded as a natural generalization of the L_p Christoffel-Minkowski problem and Lp dual Minkowski problem. We investigate and arrive at the existence of smooth solution to the (p,q)-Christoffel-Minkowski problem by a type of expanding curvature flow. Furthermore, the uniqueness result of solutions to the (p,q)-Christoffel-Minkowski problem shall be discussed.

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