Resonances for Manifolds Hyperbolic near Infinity: Optimal Lower Bounds on Order of Growth
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چکیده
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 minus one 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.
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