A rigidity estimate for maps from S2$S^2$ to S2$S^2$ via the harmonic map flow

Abstract

We show how a rigidity estimate introduced in recent work of Bernand-Mantel, Muratov and Simon can be derived using the harmonic map flow. The estimate controls how far a degree one map between 2-spheres can be from a Möbius map in terms of its energy, irrespective of whether or not the map has small tension.