Conformal Spectrum and Harmonic maps

Nikolai Nadirashvili; Yannick Sire

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arXiv · 1007.3104

Conformal Spectrum and Harmonic maps

Nikolai Nadirashvili·Yannick Sire

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Abstract

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.

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BibTeX RIS

Nikolai Nadirashvili, Yannick Sire. 2010-07-19. Conformal Spectrum and Harmonic maps. https://arxiv.org/abs/1007.3104

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