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Journal Articles Geometriae Dedicata Year : 2022

Bottom of the $L^2$ spectrum of the Laplacian on locally symmetric spaces

Abstract

We estimate the bottom of the $L^2$ spectrum of the Laplacian on locally symmetric spaces in terms of the critical exponents of appropriate Poincaré series. Our main result is the higher rank analog of a characterization due to Elstrodt, Patterson, Sullivan and Corlette in rank one. It improves upon previous results obtained by Leuzinger and Weber in higher rank.
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Dates and versions

hal-02865274 , version 1 (11-06-2020)
hal-02865274 , version 2 (22-07-2021)

Identifiers

  • HAL Id : hal-02865274 , version 2

Cite

Jean-Philippe Anker, Hong-Wei Zhang. Bottom of the $L^2$ spectrum of the Laplacian on locally symmetric spaces. Geometriae Dedicata, 2022, 216 (1), paper 3. ⟨hal-02865274v2⟩
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