Geometric eigenvalue estimates of Kuttler-Sigillito type on differential forms

Rodolphe Abou Assali

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arXiv · 2602.09876

Geometric eigenvalue estimates of Kuttler-Sigillito type on differential forms

Rodolphe Abou Assali

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Abstract

We introduce a new biharmonic Steklov problem on differential forms with Dirichlet-type boundary conditions and show that it is elliptic. We prove the existence of a discrete spectrum for this problem and give variational characterizations for eigenvalues associated to it. We establish eigenvalue estimates known as Kuttler-Sigillito inequalities, that connect the eigenvalues of different problems on differential forms with curvature quantities on the manifold.

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Rodolphe Abou Assali. 2026-02-10. Geometric eigenvalue estimates of Kuttler-Sigillito type on differential forms. https://arxiv.org/abs/2602.09876

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