# Les applications conforme-harmoniques

Abstract : On a Riemannian surface, the energy of a map into a Riemannian manifold is a conformal invariant functional, and its critical points are the harmonic maps. Our main result is a generalization of this theorem when the starting manifold is even dimensional. We then build a conformal invariant functional for the maps between two Riemannian manifolds. Its critical points then called C--harmonic are the solutions of a nonlinear elliptic PDE of order $n$, which is conformal invariant with respect to the start manifold. For the trivial case of real or complex functions of $M$, we find again the GJMS operator, with a leading part power to the $n/2$ of the Laplacian.
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https://tel.archives-ouvertes.fr/tel-00468343
Contributor : Vincent Berard <>
Submitted on : Tuesday, March 30, 2010 - 3:24:52 PM
Last modification on : Friday, June 19, 2020 - 9:22:04 AM
Long-term archiving on: : Monday, July 26, 2010 - 11:36:32 AM

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• HAL Id : tel-00468343, version 1

### Citation

Vincent Berard. Les applications conforme-harmoniques. Mathématiques [math]. Université de Strasbourg, 2010. Français. ⟨NNT : 2010STRA6160⟩. ⟨tel-00468343⟩

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