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Critical exponent and bottom of the spectrum in pinched negative curvature

Abstract : In this note, we present a new proof of the celebrated theorem of Patterson–Sullivan which relates the critical exponent of a hyperbolic manifold and the bottom of its spectrum. The proof extends to manifolds with pinched negative curvatures. It provides a sufficient criterion for the existence of isolated eigenvalues for the Laplacian on geometrically finite manifolds with pinched negative curvatures.
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https://hal.archives-ouvertes.fr/hal-01729692
Contributor : Samuel Tapie <>
Submitted on : Monday, March 12, 2018 - 5:15:05 PM
Last modification on : Friday, March 27, 2020 - 3:49:42 AM

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Thomas Roblin, Samuel Tapie. Critical exponent and bottom of the spectrum in pinched negative curvature. Mathematical Research Letters, 2015, 22 (3), pp.929 - 944. ⟨10.4310/MRL.2015.v22.n3.a15⟩. ⟨hal-01729692⟩

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