Werner Ballmann, Mayukh Mukherjee, Panagiotis Polymerakis, “On the Spectrum of Certain Hadamard Manifolds”, SIGMA, 2023, Volume 19,050, 19 pp.

On the Spectrum of Certain Hadamard Manifolds

Werner Ballmann^a, Mayukh Mukherjee^b, 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

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.

Keywords: Laplace operator, absolutely continuous spectrum, point spectrum, Hadamard manifold, asymptotically harmonic manifold.

MSC: 58J50, 53C20

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

Language: English

DOI: 10.3842/SIGMA.2023.050