Laplacian and spectral gap in regular Hilbert geometries - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Tohoku mathematical journal Année : 2014

Laplacian and spectral gap in regular Hilbert geometries

Résumé

We study the spectrum of the Finsler--Laplace operator for regular Hilbert geometries, defined by convex sets with $C^2$ boundaries. We show that for an $n$-dimensional geometry, the spectral gap is bounded above by $(n-1)^2/4$, which we prove to be the infimum of the essential spectrum. We also construct examples of convex sets with arbitrarily small eigenvalues.

Dates et versions

hal-00770217 , version 1 (04-01-2013)

Identifiants

Citer

Thomas Barthelmé, Bruno Colbois, Mickaël Crampon, Patrick Verovic. Laplacian and spectral gap in regular Hilbert geometries. Tohoku mathematical journal, 2014, 66 (3), pp.377-407. ⟨10.2748/tmj/1412783204⟩. ⟨hal-00770217⟩
112 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More