An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions

TL;DR

This paper provides a simple, elementary proof of Jensen's theorem, establishing the uniqueness of infinity harmonic functions by using finite difference approximations through maximums and minimums over small regions.

Contribution

The paper introduces an accessible proof technique for Jensen's theorem, simplifying the understanding of the uniqueness of infinity harmonic functions.

Findings

Proof simplifies understanding of Jensen's theorem

Establishes uniqueness of infinity harmonic functions

Uses finite difference approach with maximums and minimums

Abstract

We present a new, easy, and elementary proof of Jensen's Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.