Geometric eigenvalue estimates of Kuttler-Sigillito type on differential forms
Differential Geometry
2026-02-11 v1 Analysis of PDEs
Spectral Theory
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.
Cite
@article{arxiv.2602.09876,
title = {Geometric eigenvalue estimates of Kuttler-Sigillito type on differential forms},
author = {Rodolphe Abou Assali},
journal= {arXiv preprint arXiv:2602.09876},
year = {2026}
}