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.
RIGIDITY OF MINIMAL LAGRANGIAN DIFFEOMORPHISMS BETWEEN SPHERICAL CONE SURFACES
El Emam C.;Seppi A.
2022-01-01
Abstract
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.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
JEP_2022__9__581_0.pdf
Accesso aperto
Descrizione: versione pubblicata
Tipo di file:
PDF EDITORIALE
Dimensione
946 kB
Formato
Adobe PDF
|
946 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
