Lojasiewicz inequalities for almost harmonic maps near simple bubble trees

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1. Verfasser: Rupflin, Melanie
Format: Preprint
Veröffentlicht: 2021
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author Rupflin, Melanie
author_facet Rupflin, Melanie
contents We prove Lojasiewicz 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 Lojasiewicz-Simon inequalities valid near harmonic maps $\hat ω:S^2\to N$ to the singular setting whenever the bubble $\hat ω$ is attached at a point which is not a branch point.
format Preprint
id arxiv_https___arxiv_org_abs_2101_05527
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Lojasiewicz inequalities for almost harmonic maps near simple bubble trees
Rupflin, Melanie
Analysis of PDEs
Differential Geometry
58E20, 53C43
We prove Lojasiewicz 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 Lojasiewicz-Simon inequalities valid near harmonic maps $\hat ω:S^2\to N$ to the singular setting whenever the bubble $\hat ω$ is attached at a point which is not a branch point.
title Lojasiewicz inequalities for almost harmonic maps near simple bubble trees
topic Analysis of PDEs
Differential Geometry
58E20, 53C43
url https://arxiv.org/abs/2101.05527