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 language | English |
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Pages (from-to) | 4431-4470 |
Number of pages | 40 |
Journal | International Mathematics Research Notices |
Volume | 2011 |
Issue number | 19 |
DOIs | |
State | Published - 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