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Counting solutions of perturbed harmonic map equations


Kappeler, T; Latschev, J (2005). Counting solutions of perturbed harmonic map equations. L'Enseignement Mathématique. Revue Internationale. 2e Série, 51(1-2):47-85.

Abstract

In this paper we consider perturbed harmonic map equations for maps between closed Riemannian manifolds. In the case where the target manifold has negative sectional curvature we prove - among other results - that for a large class of semilinear and quasilinear perturbations, the perturbed harmonic map equations have solutions in any homotopy class of maps for which the Euler characteristic of the set of harmonic maps does not vanish. Under an additional condition, similar results hold in the case where the target manifold has nonpositive sectional curvature. The proofs are presented in an abstract setup suitable for generalizations to other situations.

Abstract

In this paper we consider perturbed harmonic map equations for maps between closed Riemannian manifolds. In the case where the target manifold has negative sectional curvature we prove - among other results - that for a large class of semilinear and quasilinear perturbations, the perturbed harmonic map equations have solutions in any homotopy class of maps for which the Euler characteristic of the set of harmonic maps does not vanish. Under an additional condition, similar results hold in the case where the target manifold has nonpositive sectional curvature. The proofs are presented in an abstract setup suitable for generalizations to other situations.

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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
Language:English
Date:2005
Deposited On:18 Feb 2010 14:13
Last Modified:06 Dec 2017 20:46
Publisher:Fondation L'Enseignement Mathématique
ISSN:0013-8584
Related URLs:http://retro.seals.ch/digbib/vollist?UID=ensmat-001

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