Comptes Rendus
Partial differential equations/Differential geometry
Eigenvalue and gap estimates of isometric immersions for the Dirichlet-to-Neumann operator acting on p-forms
Comptes Rendus. Mathématique, Volume 357 (2019) no. 2, pp. 180-187.

In this paper, we study the first eigenvalue of the Dirichlet-to-Neumann operator acting on differential forms of a Riemannian manifold with boundary isometrically immersed in some Euclidean space. We give a lower bound of the integral energy of p-forms in terms of its first eigenvalue associated with (p1)-forms. We also find a lower bound for the gap between two consecutive first eigenvalues in terms of the curvature of the boundary.

Dans cet article, nous étudions la première valeur propre de l'opérateur de Dirichlet-à-Neumann agissant sur les formes différentielles d'une variété riemannienne à bord plongée isométriquement dans un espace euclidien. Nous obtenons une borne inférieure de l'énergie des p-formes en termes de sa première valeur propre associée aux (p1)-formes. Nous trouvons aussi une borne inférieure pour l'écart entre deux premières valeurs propres consécutives par rapport à la courbure de la frontière.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2019.01.006

Deborah Michel 1

1 Laboratoire de mathématiques Raphaël-Salem, UMR 6085 CNRS–Université de Rouen, avenue de l'Université, BP 12, Technopôle du Madrillet, 76801 Saint-Étienne-du-Rouvray, France
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Deborah Michel. Eigenvalue and gap estimates of isometric immersions for the Dirichlet-to-Neumann operator acting on p-forms. Comptes Rendus. Mathématique, Volume 357 (2019) no. 2, pp. 180-187. doi : 10.1016/j.crma.2019.01.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.01.006/

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