David Borthwick
Sharp geometric upper bounds on resonances for surfaces with hyperbolic ends.
Wed, 06/30/2010 - 15:01 — SomNambulAuthors: David Borthwick
Subjects: Spectral Theory
AbstractWe establish a sharp geometric constant for the upper bound on the resonance
counting function for surfaces with hyperbolic ends. An arbitrary metric is
allowed within some compact core, and the ends may be of hyperbolic planar,
funnel, or cusp type. The constant in the upper bound depends only on the
volume of the core and the length parameters associated to the funnel or
hyperbolic planar ends.Sharp upper bounds on resonances for perturbations of hyperbolic space.
Wed, 10/14/2009 - 11:03 — SomNambulAuthors: David Borthwick
Subjects: Spectral Theory
AbstractFor certain compactly supported metric and/or potential perturbations of the
Laplacian on $\mathbb{H}^{n+1}$, we establish an upper bound on the resonance
counting function with an explicit constant that depends only on the dimension,
the radius of the unperturbed region in $\mathbb{H}^{n+1}$, and the volume of
the metric perturbation. This constant is shown to be sharp in the case of
scattering by a spherical obstacle.Sharp upper bounds on resonances for perturbations of hyperbolic space.
Wed, 10/14/2009 - 11:03 — SomNambulAuthors: David Borthwick
Subjects: Spectral Theory
AbstractFor certain compactly supported metric and/or potential perturbations of the
Laplacian on $\mathbb{H}^{n+1}$, we establish an upper bound on the resonance
counting function with an explicit constant that depends only on the dimension,
the radius of the unperturbed region in $\mathbb{H}^{n+1}$, and the volume of
the metric perturbation. This constant is shown to be sharp in the case of
scattering by a spherical obstacle.
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