Article (Scientific journals)
Rigidity of minimal Lagrangian diffeomorphisms between spherical cone surfaces
El Emam, Christian; Seppi, Andrea
2022In Journal de l'École Polytechnique. Mathématiques, 9, p. 581-600
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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 :
9
Pages :
581-600
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 22 January 2021

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