Resonances for manifolds hyperbolic near infinity: Optimal lower bounds on order of growth

D. Borthwick, T. J. Christiansen, P. D. Hislop, P. A. Perry

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Suppose that (X, g) is a conformally compact (n+1)-dimensional manifold that is hyperbolic near infinity in the sense that the sectional curvatures of g are identically equal to-1 outside of a compact set K⊂X. We prove that the counting function for the resolvent resonances has maximal order of growth (n+1) generically for such manifolds. This is achieved by constructing explicit examples of manifolds hyperbolic at infinity for which the resonance counting function obeys optimal lower bounds.

Original languageEnglish
Pages (from-to)4431-4470
Number of pages40
JournalInternational Mathematics Research Notices
Volume2011
Issue number19
DOIs
StatePublished - 2011

Bibliographical note

Funding Information:
The authors are grateful for support from the Mathematical Sciences Research Institute and the

Funding Information:
DB supported in part by NSF grant DMS-0901937; TC supported in part by NSF grants DMS-0500267 and DMS-1001156; PDH supported in part by NSF grant DMS-0803379; PP supported in part by NSF grant DMS-0710477.

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of 'Resonances for manifolds hyperbolic near infinity: Optimal lower bounds on order of growth'. Together they form a unique fingerprint.

Cite this