Abstract
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.
Citation
Thomas Barthelmé. Bruno Colbois. Mickaël Crampon. Patrick Verovic. "Laplacian and spectral gap in regular Hilbert geometries." Tohoku Math. J. (2) 66 (3) 377 - 407, 2014. https://doi.org/10.2748/tmj/1412783204
Information