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• W2969331369 startingPage "667" @default.
• W2969331369 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 $${mathbb {S}}^2$$ differ significantly from the properties of those induced from $${mathbb {S}}^m$$ with $$m>2$$. This feature appears to be novel and needs to be taken into account in the existing proofs of the sharp upper bounds for the first nonzero eigenvalue of the Laplacian on the 2-torus and the Klein bottle. In the present paper we address this issue and give a detailed overview of the complete proofs of these upper bounds following the works of Nadirashvili, Jakobson–Nadirashvili–Polterovich, El Soufi–Giacomini–Jazar, Nadirashvili–Sire and Petrides." @default.
• W2969331369 created "2019-08-29" @default.
• W2969331369 creator A5025613783 @default.
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• W2969331369 date "2019-08-21" @default.
• W2969331369 modified "2023-10-06" @default.
• W2969331369 title "On branched minimal immersions of surfaces by first eigenfunctions" @default.
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• W2969331369 doi "https://doi.org/10.1007/s10455-019-09683-8" @default.
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