THE LAPLACE SPECTRUM ON CONFORMALLY COMPACT MANIFOLDS
Journal article, 2024

We consider the spectrum of the Laplace operator acting on L-p over a conformally compact manifold for 1 < p < infinity. We prove that for p not equal 2 this spectrum always contains an open region of the complex plane. We further show that the spectrum is contained within a certain parabolic region of the complex plane. These regions depend on the value of p, the dimension of the manifold, and the values of the sectional curvatures approaching the boundary.

Author

Nelia Charalambous

University of Cyprus

Julie Rowlett

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Transactions of the American Mathematical Society

0002-9947 (ISSN) 1088-6850 (eISSN)

Vol. 377 5 3373-3395

Geometric analysis and applications to microbe ecology

Swedish Research Council (VR) (2018-03873), 2019-01-01 -- 2022-12-31.

Subject Categories

Mathematics

DOI

10.1090/tran/9107

More information

Latest update

5/25/2024