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