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Abstract 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… Click to show full abstract
Abstract 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 ( p − 1 ) -forms. We also find a lower bound for the gap between two consecutive first eigenvalues in terms of the curvature of the boundary.
Keywords:
neumann operator;
eigenvalue gap;
operator acting;
dirichlet neumann
Journal Title: Comptes Rendus Mathematique
Year Published: 2019
Link to full text (if available)
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Journal Title: Comptes Rendus Mathematique
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!