Comptes Rendus
no. 11
Differential geometry
Moser-type results in Riemannian product spaces
[Résultats à la Moser dans les espaces produit de Riemann]

Présenté par : Enrico Bombieri

Arlandson M.S. Oliveira1 ; Henrique F. de Lima1
1 Departamento de Matemática, Universidade Federal de Campina Grande, 58429-970 Campina Grande, Paraíba, Brazil
Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1017-1021.

Dans cette courte Note, nous obtenons de nouvelles extensions d'un théorème classique de Moser [8] comme application du principe bien connu du maximum généralisé de Omori–Yau. Plus précisément, soit u une fonction lisse définissant un graphe Σ(u) entier, CMC, construit sur une fibre Mn d'un espace produit de Riemann du type R×Mn. Nous montrons alors que, sous des contraintes convenables sur la norme du gradient de u, cette fonction doit en fait être constante.

In this short paper, as applications of the well-known generalized maximum principle of Omori–Yau, we obtain new extensions of a classical theorem due to Moser [8]. More precisely, under suitable constraints on the norm of the gradient of the smooth function u that defines an entire CMC graph Σ(u) constructed over a fiber Mn of a Riemannian product space of the type R×Mn, we show that u must actually be constant.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.09.001
Mots clés : Riemannian product spaces, Complete hypersurfaces, Mean curvature, Angle function, Entire graphs
Arlandson M.S. Oliveira 1 ; Henrique F. de Lima 1

1 Departamento de Matemática, Universidade Federal de Campina Grande, 58429-970 Campina Grande, Paraíba, Brazil 
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Arlandson M.S. Oliveira; Henrique F. de Lima. Moser-type results in Riemannian product spaces. Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1017-1021. doi : 10.1016/j.crma.2015.09.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.09.001/

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