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Article Dans Une Revue Moscow Mathematical Journal Année : 2015

Conformal Spectrum and Harmonic maps

Résumé

This paper is devoted to the study of the conformal spectrum (and more precisely the first eigenvalue) of the Laplace-Beltrami operator on a smooth connected compact Riemannian surface without boundary, endowed with a conformal class. We give a constructive proof of a critical metric which is smooth except at some conical singularities and maximizes the first eigenvalue in the conformal class of the background metric. We also prove that the map associating a finite number of eigenvectors of the maximizing $\lambda_1$ into the sphere is harmonic, establishing a link between conformal spectrum and harmonic maps.

Dates et versions

hal-01338001 , version 1 (27-06-2016)

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Nikolai Nadirashvili, Yannick Sire. Conformal Spectrum and Harmonic maps. Moscow Mathematical Journal, 2015, 15 (1), pp.123--140, 182. ⟨10.17323/1609-4514-2015-15-1-123-140⟩. ⟨hal-01338001⟩
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