Comptes Rendus
Differential Geometry
Extension of Reilly formula with applications to eigenvalue estimates for drifting Laplacians
[Extension de la formule de Reilly avec applications aux estimées de valeurs propres pour les laplaciens avec dérive]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1203-1206.

In this Note, we extend the Reilly formula for drifting Laplacian operator and apply it to study eigenvalue estimate for drifting Laplacian operators on compact Riemannian manifolds' boundary. Our results on eigenvalue estimates extend previous results of Reilly and Choi and Wang.

Dans cette Note, nous étendons la formule de Reilly au cas des opérateurs Laplaciens avec dérive, et l'appliquons à l'étude d'estimées de valeurs propres pour de tels opérateurs sur des variétés riemanniennes compactes à bord. Nos estimées généralisent des résultats antérieurs de Reilly ainsi que de Choi et Wang.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.10.003

Li Ma 1 ; Sheng-Hua Du 2

1 Department of Mathematics, Henan Normal University, Xinxiang, 453007, China
2 Department of Mathematics, Tsinghua University, Beijing, 100084, China
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Li Ma; Sheng-Hua Du. Extension of Reilly formula with applications to eigenvalue estimates for drifting Laplacians. Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1203-1206. doi : 10.1016/j.crma.2010.10.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.003/

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The research is partially supported by the National Natural Science Foundation of China 10631020 and SRFDP 20090002110019.

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