The Gradient Flow of Infinity-Harmonic Potentials

TL;DR

This paper investigates the behavior of streamlines in infinity-harmonic functions within planar convex rings, characterizing points where streamlines meet and analyzing the gradient's properties along these paths.

Contribution

It provides a detailed characterization of streamline meeting points and gradient behavior for infinity-harmonic functions in convex polygons and rings.

Findings

Points where streamlines meet lie on specific curves.

Gradient has constant norm along streamlines outside meeting points.

Includes analysis of convex polygons and rings.

Abstract

We study the streamlines of $\infty$-harmonic functions in planar convex rings. We include convex polygons. The points where streamlines can meet are characterized: they lie on certain curves. The gradient has constant norm along streamlines outside the set of meeting points, the infinity-ridge.