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Conformal Spectrum and Harmonic maps | | Nikolai Nadirashvili
; Yannick Sire
; | | Date: |
19 Jul 2010 | | 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. | | Source: | arXiv, 1007.3104 | | Services: | Forum | Review | PDF | Favorites | |
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