Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 050, 19 pages      arXiv:2301.10986      https://doi.org/10.3842/SIGMA.2023.050
Contribution to the Special Issue on Differential Geometry Inspired by Mathematical Physics in honor of Jean-Pierre Bourguignon for his 75th birthday

On the Spectrum of Certain Hadamard Manifolds

Werner Ballmann ^a, Mayukh Mukherjee ^b and Panagiotis Polymerakis ^c
a) Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
^b) Indian Institute of Technology Bombay, Powai, 400076 Maharashtra, India
^c) Department of Mathematics, University of Thessaly, 3rd km Old National Road Lamia-Athens, 35100 Lamia, Greece

Received January 27, 2023, in final form July 14, 2023; Published online July 23, 2023

Abstract
We show the absolute continuity of the spectrum and determine the spectrum as a set for two classes of Hadamard manifolds and for specific domains and quotients of one of the classes.

Key words: Laplace operator; absolutely continuous spectrum; point spectrum; Hadamard manifold; asymptotically harmonic manifold.

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