Karpukhin, Mikhail;
Vinokurov, Denis;
(2022)
The first eigenvalue of the Laplacian on orientable surfaces.
Mathematische Zeitschrift
, 301
(3)
pp. 2733-2746.
10.1007/s00209-022-03009-4.
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Abstract
The famous Yang–Yau inequality provides an upper bound for the first eigenvalue of the Laplacian on an orientable Riemannian surface solely in terms of its genus γ and the area. Its proof relies on the existence of holomorhic maps to CP1 of low degree. Very recently, Ros was able to use certain holomorphic maps to CP2 in order to give a quantitative improvement of the Yang–Yau inequality for γ = 3. In the present paper, we generalize Ros’ argument to make use of holomorphic maps to CPn for any n > 0. As an application, we obtain a quantitative improvement of the Yang–Yau inequality for all genera except for γ = 4, 6, 8, 10, 14.
| Type: | Article |
|---|---|
| Title: | The first eigenvalue of the Laplacian on orientable surfaces |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00209-022-03009-4 |
| Publisher version: | https://doi.org/10.1007/s00209-022-03009-4 |
| 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. |
| 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-pp.ucl.ac.uk/id/eprint/10201309 |
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