The chord Gauss curvature flow and its $L_{p}$ chord Minkowski problem

TL;DR

This paper addresses the $L_{p}$ chord Minkowski problem by establishing a new existence result for solutions using a nonlocal Gauss curvature flow, extending previous work to a broader range of p values.

Contribution

It introduces a novel nonlocal Gauss curvature flow approach to solve the $L_{p}$ chord Minkowski problem for p > -n, p ≠ 0, expanding the scope of existing solutions.

Findings

Established existence of solutions for the $L_{p}$ chord Minkowski problem.

Extended previous results to a wider range of p values.

Developed a nonlocal curvature flow method for solving geometric problems.

Abstract

In this paper, the $L_{p}$ chord Minkowski problem is concerned. Based on the results showed in \cite{HJ23}, we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvature flow for $p>-n$ with $p\neq 0$.