Abstract
We prove the following conjecture recently formulated by Jakobson, Nadirashvili, and Polterovich (see [15, Conjecture 1.5, page 383]). On the Klein bottle , the metric of revolution , , is the unique extremal metric of the first eigenvalue of the Laplacian viewed as a functional on the space of all Riemannian metrics of given area. The proof leads us to study a Hamiltonian dynamical system that turns out to be completely integrable by quadratures
Citation
Ahmad El Soufi. Hector Giacomini. Mustapha Jazar. "A unique extremal metric for the least eigenvalue of the Laplacian on the Klein bottle." Duke Math. J. 135 (1) 181 - 202, 1 October 2006. https://doi.org/10.1215/S0012-7094-06-13514-7
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