Łojasiewicz inequalities for almost harmonic maps near simple bubble trees

  • Melanie Rupflin

    University of Oxford, Oxford, UK
Łojasiewicz inequalities for almost harmonic maps near simple bubble trees cover

A subscription is required to access this article.

Abstract

We prove Łojasiewicz inequalities for the harmonic map energy for maps from surfaces of positive genus into general analytic target manifolds which are close to simple bubble trees and as a consequence obtain new results on the convergence of harmonic map flow and on the energy spectrum of harmonic maps with small energy. Our results and techniques are not restricted to particular targets or to integrable settings and we are able to lift general Łojasiewicz–Simon inequalities valid near harmonic maps to the singular setting whenever the bubble is attached at a point which is not a branch point.

Cite this article

Melanie Rupflin, Łojasiewicz inequalities for almost harmonic maps near simple bubble trees. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2024), published online first

DOI 10.4171/AIHPC/131