Karpukhin, Mikhail A;
(2015)
Upper Bounds for the First Eigenvalue of the Laplacian on Non-Orientable Surfaces.
International Mathematics Research Notices
, 2016
(20)
pp. 6200-6209.
10.1093/imrn/rnv345.
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Abstract
In 1980 Yang and Yau [18] proved the celebrated upper bound for the first eigenvalue on an orientable surface of genus γ. Later Li and Yau [12] gave a simple proof of this bound by introducing the concept of conformal volume of a Riemannian manifold. In the same paper they proposed an approach for obtaining a similar estimate for non-orientable surfaces. In the present paper we formalize their argument and improve the bounds stated in.
| Type: | Article |
|---|---|
| Title: | Upper Bounds for the First Eigenvalue of the Laplacian on Non-Orientable Surfaces |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imrn/rnv345 |
| Publisher version: | https://doi.org/10.1093/imrn/rnv345 |
| Language: | English |
| Additional information: | This version is the author-accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Non-orientable surfaces, eigenvalues of the Laplacian. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10201292 |
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