Relative energy gap for harmonic maps of Riemann surfaces into real analytic Riemannian manifolds

Abstract

We extend the well-known Sacks–Uhlenbeck energy gap result for harmonic maps from closed Riemann surfaces into closed Riemannian manifolds from the case of maps with small energy (thus near a constant map), to the case of harmonic maps with high absolute energy but small energy relative to a reference harmonic map.