A flow method for a generalization of $L_{p}$ Christofell-Minkowski problem

TL;DR

This paper introduces a flow-based approach to generalize the $L_{p}$-Christoffel-Minkowski problem, establishing long-term existence and smooth solutions under certain conditions.

Contribution

It proposes a novel anisotropic curvature flow method to address the generalized $L_{p}$-Christoffel-Minkowski problem, extending previous results.

Findings

Proved long-time existence of the curvature flow.

Established existence of smooth solutions for specific initial data.

Extended the classical problem to a more general anisotropic setting.

Abstract

In this paper, a generalization of the $L_{p}$-Christoffel-Minkowski problem is studied. We consider an anisotropic curvature flow and derive the long-time existence of the flow. Then under some initial data, we obtain the existence of smooth solutions to this problem for $c=1$.