Comptes Rendus
no. 11
Differential geometry
Moser-type results in Riemannian product spaces

Presented by: 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.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.09.001
Keywords: 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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