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Maximization of the Fundamental Tone on the Klein Bottle | | Donato Cianci
; Vladimir Medvedev
; | | Date: |
16 Nov 2017 | | Abstract: | In this expository paper we provide a complete proof of the fact that the
first non-zero eigenvalue of the Laplacian on a Klein bottle is maximized by
the bipolar Lawson surface au_{3,1}. While this result follows from the
earlier work of Jakobson-Nadirashvili-Polterovich, El Soufi-Giacomini-Jazar,
Nadirashvili-Sire and Petrides, its proof has never been written up in full.
The goal of this note is to close this gap in the literature. In particular, we
generalize certain results of El Soufi and Ilias regarding conformal volume to
metrics with conical singularities and prove continuity of the k-conformal
eigenvalue functional with respect to conformal classes. | | Source: | arXiv, 1711.5916 | | Services: | Forum | Review | PDF | Favorites | |
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