@article{c696aa7dc57540f1aaa8ee4ecec0d5c4,

title = "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.",

keywords = "Harmonic maps, {\L}ojasiewicz-Simon gradient inequality",

author = "Feehan, {Paul M.N.}",

note = "Funding Information: Received by the editors September 12, 2017. 2010 Mathematics Subject Classification. Primary 58E20; Secondary 37D15. Key words and phrases. Harmonic maps, Lojasiewicz–Simon gradient inequality. The author was partially supported by National Science Foundation grant DMS-1510064 and the Oswald Veblen Fund and Fund for Mathematics (Institute for Advanced Study, Princeton) during the preparation of this article. Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

year = "2018",

month = jul,

doi = "10.1090/proc/14013",

language = "English (US)",

volume = "146",

pages = "3179--3190",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "7",

}