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Laplacian and spectral gap in regular Hilbert geometries
Auteur(s)
Date Issued
2014-9-19
Journal
Tohoku Math. J.
No
66
From page
377
To page
407
Abstract
We study the spectrum of the Finsler--Laplace operator for regular Hilbert geometries, defined by convex sets with C2 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.
Other version
https://projecteuclid.org/euclid.tmj/1412783204
Publication type
journal article
