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Perturbations of the harmonic map equation


Kappeler, T (2002). Perturbations of the harmonic map equation. In: Journées "Équations aux Dérivées Partielles" (Forges-les-Eaux, 2002). Nantes: University of Nantes, Ex No. IX, 8.

Abstract

We consider perturbations of the harmonic map equation in the case where the source and target manifolds are closed Riemannian manifolds and the latter is, in addition, of nonpositive sectional curvature. For any semilinear and, under some extra conditions, quasilinear perturbation, the space of classical solutions within a homotopy class is proved to be compact. For generic perturbations the set of solutions is finite and we present a count of this set. An important ingredient for our analysis is a new inequality for maps in a given homotopy class which can be viewed as a version of the Poincaré inequality for such maps.

Abstract

We consider perturbations of the harmonic map equation in the case where the source and target manifolds are closed Riemannian manifolds and the latter is, in addition, of nonpositive sectional curvature. For any semilinear and, under some extra conditions, quasilinear perturbation, the space of classical solutions within a homotopy class is proved to be compact. For generic perturbations the set of solutions is finite and we present a count of this set. An important ingredient for our analysis is a new inequality for maps in a given homotopy class which can be viewed as a version of the Poincaré inequality for such maps.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2002
Deposited On:18 Feb 2010 13:14
Last Modified:05 Apr 2016 13:25
Publisher:University of Nantes
ISBN:2-86939-188-9
Free access at:Official URL. An embargo period may apply.
Official URL:http://www.math.sciences.univ-nantes.fr/edpa/2002/pdf/kapp.pdf
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1968205

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