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 entier, CMC, construit sur une fibre d'un espace produit de Riemann du type . 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 constructed over a fiber of a Riemannian product space of the type , we show that u must actually be constant.
Accepté le :
Publié le :
Arlandson M.S. Oliveira 1 ; Henrique F. de Lima 1
@article{CRMATH_2015__353_11_1017_0, author = {Arlandson M.S. Oliveira and Henrique F. de Lima}, title = {Moser-type results in {Riemannian} product spaces}, journal = {Comptes Rendus. Math\'ematique}, pages = {1017--1021}, publisher = {Elsevier}, volume = {353}, number = {11}, year = {2015}, doi = {10.1016/j.crma.2015.09.001}, language = {en}, }
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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