Cianci, Donato;
Karpukhin, Mikhail;
Medvedev, Vladimir;
(2019)
On branched minimal immersions of surfaces by first eigenfunctions.
Annals of Global Analysis and Geometry
, 56
pp. 667-690.
10.1007/s10455-019-09683-8.
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Abstract
It was proved by Montiel and Ros that for each conformal structure on a compact surface there is at most one metric which admits a minimal immersion into some unit sphere by first eigenfunctions. We generalize this theorem to the setting of metrics with conical singularities induced from branched minimal immersions by first eigenfunctions into spheres. Our primary motivation is the fact that metrics realizing maxima of the first nonzero Laplace eigenvalue are induced by minimal branched immersions into spheres. In particular, we show that the properties of such metrics induced from
| Type: | Article |
|---|---|
| Title: | On branched minimal immersions of surfaces by first eigenfunctions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s10455-019-09683-8 |
| Publisher version: | https://doi.org/10.1007/s10455-019-09683-8 |
| 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: | Spectral theory, Branched minimal immersions, Maximal metrics Eigenvalue bounds |
| 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/10201295 |
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