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 (1981) 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.

11 pages, incorporating final galley proof corrections. To appear in Proceedings of the American Mathematical Society. arXiv admin note: text overlap with arXiv:1510.03817

References in corpus (2)

• Some aspects of Dirac-harmonic maps with curvature term
• The heat flow for the full bosonic string

Cited by in corpus (1)

• Lojasiewicz-Simon gradient inequalities for analytic and Morse-Bott functions on Banach spaces