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Colbois, Bruno
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Colbois, Bruno
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Professeur ordinaire
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Bruno.Colbois@unine.ch
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- PublicationAccès libreLaplacian and spectral gap in regular Hilbert geometries(2014-9-19)
;Barthelmé, Thomas; ;Crampon, MickaelVerovic, PatrickWe 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.