%0 Journal Article
%T Conformal Spectrum and Harmonic maps
%+ Institut de Mathématiques de Marseille (I2M)
%A Nadirashvili, Nikolai
%A Sire, Yannick
%< avec comité de lecture
%@ 1609-3321
%J Moscow Mathematical Journal
%I Independent University of Moscow
%V 15
%N 1
%P 123--140, 182
%8 2015
%D 2015
%Z 1007.3104
%R 10.17323/1609-4514-2015-15-1-123-140
%K Eigenvalues
%K isoperimettic inequalities
%Z 35P15
%Z Mathematics [math]/Differential Geometry [math.DG]Journal articles
%X 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.
%G English
%L hal-01338001
%U https://hal.science/hal-01338001
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-