March 3, 2026Open Access

Geometric eigenvalue estimates of Kuttler-Sigillito type on differential forms

Key Points

The introduction of the biharmonic Steklov problem leads to a discrete spectrum for eigenvalues, revealing important structural properties.
Eigenvalue estimates are characterized variationally, connecting spectral properties with geometric aspects of the underlying manifold.
This study highlights the relationship between curvature quantities and eigenvalues, deepening our understanding of differential forms.
The framework presents new elliptic behavior in the biharmonic problem, implying broader applications in mathematical physics.

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.

Geometric eigenvalue estimates of Kuttler-Sigillito type on differential forms

Key Points

Abstract

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