Regularity of Wave-Maps in dimension 2+1

TL;DR

This paper proves a global regularity result for wave-maps from 2+1 dimensional spacetime into general compact manifolds, extending previous work to a broader class of target spaces.

Contribution

It establishes a Sacks-Uhlenbeck/Struwe type regularity theorem for wave-maps in 2+1 dimensions with general compact targets, broadening the scope of known regularity results.

Findings

Global regularity for wave-maps in 2+1 dimensions

Extension to general compact target manifolds

Advancement of regularity theory in geometric wave equations

Abstract

In this article we prove a Sacks-Uhlenbeck/Struwe type global regularity result for wave-maps $\Phi:\mathbb{R}^{2+1}\to\mathcal{M}$ into general compact target manifolds $\mathcal{M}$.