[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 :
Mathématiques
Auteur, co-auteur :
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
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Rigidity of minimal Lagrangian diffeomorphisms between spherical cone surfaces
Date de publication/diffusion :
10 mars 2022
Titre du périodique :
Journal de l'École Polytechnique. Mathématiques
ISSN :
2429-7100
eISSN :
2270-518X
Maison d'édition :
Éditions de l'École Polytechnique, Palaiseau, France
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