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

SIGMA 19 (2023), 050, 19 pages      arXiv:2301.10986
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

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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