A flow approach to the Orlicz-Minkowski problem for torsional rigidity

TL;DR

This paper introduces a flow-based method to solve the Orlicz-Minkowski problem for torsional rigidity, extending classical results and establishing new existence theorems for solutions involving general measures.

Contribution

It presents a novel flow approach to address the Orlicz-Minkowski problem for torsional rigidity, broadening the scope of solvable cases beyond previous methods.

Findings

Established existence of solutions for general measures

Extended classical Minkowski problem to Orlicz setting

Developed a flow method for this geometric problem

Abstract

In this paper the Orlicz-Minkowski problem for torsional rigidity, a generalization of the classical Minkowski problem, is studied. Using the flow method, we obtain a new existence result of solutions to this problem for general measures.