Anisotropic flow, entropy and $L^p$-Minkowski problem

TL;DR

This paper introduces a straightforward approach using anisotropic flows to establish the existence of weak solutions for Lutwak's $L^p$-Minkowski problem on the sphere, complementing previous methods.

Contribution

It presents a simple, natural argument leveraging anisotropic flows to prove existence results for the $L^p$-Minkowski problem, offering an alternative to prior techniques.

Findings

Existence of weak solutions to Lutwak's $L^p$-Minkowski problem on $S^n$.

Anisotropic flows can be effectively used to prove geometric problem solutions.

Provides a new, simpler proof method compared to previous approaches.

Abstract

We provide a natural simple argument using anistropic flows to prove the existence of weak solutions to Lutwak's $L^p$-Minkowski problem on $S^n$ which were obtained by other methods.