Rigidity of minimal Lagrangian diffeomorphisms between spherical cone surfaces

El Emam, Christian; Seppi, Andrea

doi:10.5802/jep.190

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Rigidity of minimal Lagrangian diffeomorphisms between spherical cone surfaces

El Emam, Christian; Seppi, Andrea

2022 • In Journal de l'École Polytechnique. Mathématiques, 9, p. 581-600

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https://hdl.handle.net/10993/45778

DOI
10.5802/jep.190

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Keywords :

Differential geometry; Spherical geometry; Cone singularities; Minimal Lagrangian maps

Abstract :

[en] We prove that any minimal Lagrangian diffeomorphism between two closed spherical surfaces with cone singularities is an isometry, without any assumption on the multiangles of the two surfaces. As an application, we show that every branched immersion of a closed surface of constant positive Gaussian curvature in Euclidean three-space is a branched covering onto a round sphere, thus generalizing the classical rigidity theorem of Liebmann to branched immersions.

Disciplines :

Mathematics

Author, co-author :

El Emam, Christian ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

Seppi, Andrea; Centre National de la Recherche Scientifique - CNRS > Institut Fourier, Université Grenoble Alpes

External co-authors :

yes

Language :

English

Title :

Rigidity of minimal Lagrangian diffeomorphisms between spherical cone surfaces

Publication date :

10 March 2022

Journal title :

Journal de l'École Polytechnique. Mathématiques

ISSN :

2270-518X

Publisher :

Éditions de l'École Polytechnique, Palaiseau, France

Volume :

Pages :

581-600

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBilu :

since 22 January 2021

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