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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 -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 -formes. Nous trouvons aussi une borne inférieure pour l'écart entre deux premières valeurs propres consécutives par rapport à la courbure de la frontière.
Michel, Deborah 1
@article{CRMATH_2019__357_2_180_0,
author = {Michel, Deborah},
title = {Eigenvalue and gap estimates of isometric immersions for the {Dirichlet-to-Neumann} operator acting on \protect\emph{p}-forms},
journal = {Comptes Rendus. Math\'ematique},
pages = {180--187},
publisher = {Elsevier},
volume = {357},
number = {2},
year = {2019},
doi = {10.1016/j.crma.2019.01.006},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2019.01.006/}
}
TY - JOUR AU - Michel, Deborah TI - Eigenvalue and gap estimates of isometric immersions for the Dirichlet-to-Neumann operator acting on p-forms JO - Comptes Rendus. Mathématique PY - 2019 SP - 180 EP - 187 VL - 357 IS - 2 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2019.01.006/ DO - 10.1016/j.crma.2019.01.006 LA - en ID - CRMATH_2019__357_2_180_0 ER -
%0 Journal Article %A Michel, Deborah %T Eigenvalue and gap estimates of isometric immersions for the Dirichlet-to-Neumann operator acting on p-forms %J Comptes Rendus. Mathématique %D 2019 %P 180-187 %V 357 %N 2 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2019.01.006/ %R 10.1016/j.crma.2019.01.006 %G en %F CRMATH_2019__357_2_180_0
Michel, Deborah. Eigenvalue and gap estimates of isometric immersions for the Dirichlet-to-Neumann operator acting on p-forms. Comptes Rendus. Mathématique, Tome 357 (2019) no. 2, pp. 180-187. doi : 10.1016/j.crma.2019.01.006. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2019.01.006/
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