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Perturbations of the harmonic map equation


Kappeler, T; Kuksin, S; Schroeder, V (2003). Perturbations of the harmonic map equation. Communications in Contemporary Mathematics, 5(4):629-669.

Abstract

We consider perturbations of the harmonic map equation in the case where the target manifold is a closed Riemannian manifold 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. 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 target manifold is a closed Riemannian manifold 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. 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:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Harmonic maps; nonpositives sectional curvature; short homotopies
Language:English
Date:2003
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:25
Publisher:World Scientific Publishing
ISSN:0219-1997
Additional Information:Electronic version of an article published as Commun. Contemp. Math. 5 (2003), no. 4 [http://dx.doi.org/10.1142/S0219199703001087] © 2003 copyright World Scientific Publishing Company [http://www.worldscinet.com/ccm/ccm.shtml]
Publisher DOI:https://doi.org/10.1142/S0219199703001087
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2003212
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1063.58012

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