An expanding curvature flow and the (p,q)-Christoffel-Minkowski problems
Differential Geometry
2024-06-26 v2 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2203.05105,
title = {An expanding curvature flow and the (p,q)-Christoffel-Minkowski problems},
author = {Bin Chen and Jingshi Cui and Peibiao Zhao},
journal= {arXiv preprint arXiv:2203.05105},
year = {2024}
}
Comments
19 pages