Prescription de la multiplicit\'e des valeurs propres du laplacien de Hodge-de Rham

TL;DR

This paper demonstrates that on high-dimensional compact manifolds, one can prescribe the volume and specific parts of the spectrum of the Hodge Laplacian on p-forms, including eigenvalue multiplicities.

Contribution

It introduces a method to prescribe the volume and finite spectral data, including eigenvalue multiplicities, of the Hodge Laplacian on manifolds of dimension greater than 6.

Findings

Prescribes volume and finite spectral data on manifolds

Can specify multiplicity of first eigenvalues

Applicable to manifolds with dimension > 6

Abstract

On any compact manifold of dimension greater than 6, we prescribe the volume and any finite part of the spectrum Hodge Laplacian acting on $p$-form for $1\leq p<\frac n2$. In particular, we prescribe the multiplicity of the first eigenvalues.