The L_p dual Christoffel-Minkowski problem for 1

2025/04/07 by Cabezas-Moreno, Carlos, Hu, Jinrong
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.04931

Abstract

In this paper, we investigate an L_p Christoffel-Minkowski-type problem that prescribes a class of L_p geometric measures, which are mixtures of the k-th area measure and the q-th dual curvature measure. By establishing a gradient estimate, we obtain the existence of an even, smooth, strictly convex solution to this problem for 1 < p < q ≤ k + 1, where 1 ≤ k ≤ n and n ≥ 1.

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• The L_p-dual Christoffel-Minkowski problem for the case p≥ q
• An expanding curvature flow and the (p,q)-Christoffel-Minkowski problems
• The L_p dual Minkowski problem for p>1 and q>0
• The L_p dual Minkowski problem for unbounded closed convex sets
• Uniqueness and continuity of the solution to L_p dual Minkowski problem