Geodesic
Geometry
The lower and upper bounds of the first eigenvalues for the bi-harmonic operator on manifolds
[Bornes inférieures et supérieures des premières valeurs propres de l'opérateur bi-harmonique sur une variété]

Présenté par : the Editorial Board

Zhang, Liuwei1
1 Department of Mathematics, Tongji University, Shanghai, 200092, PR China
Comptes Rendus. Mathématique, Tome 353 (2015) no. 8, pp. 735-740.

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In this paper, we will estimate the lower bounds and upper bounds of the first eigenvalues for bi-harmonic operators on manifolds through Reilly's and Bochner's formulae, respectively.

Dans cette Note, nous donnons des minorants et majorants des premières valeurs propres de l'opérateur bi-harmonique sur une variété riemannienne, compacte, connexe, en utilisant respectivement les formules de Reilly et de Bochner.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.06.001

Zhang, Liuwei 1

1 Department of Mathematics, Tongji University, Shanghai, 200092, PR China 
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Zhang, Liuwei. The lower and upper bounds of the first eigenvalues for the bi-harmonic operator on manifolds. Comptes Rendus. Mathématique, Tome 353 (2015) no. 8, pp. 735-740. doi : 10.1016/j.crma.2015.06.001. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2015.06.001/

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☆ This work is supported by the National Natural Science Foundation of China (No. 11201400).