Geometric eigenvalue estimates of Kuttler-Sigillito type on differential forms

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Rodolphe Abou Assali
DOI: 10.48550/arxiv.2602.09876
Cited by: 0

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, which connect the eigenvalues of different problems on differential forms with curvature quantities on the manifold.

Fields of Study & Subjects

Spectral Theory in Mathematical Physics Geometric Analysis and Curvature Flows Nonlinear Partial Differential Equations

Publication details

Journal / source
arXiv (Cornell University)
Publication date
10 February 2026
Language
EN
Document type
Preprint