activity
19972004
most citedSelberg's zeta function and the spectral geometry of geometrically finite hyperbolic surfaces

2 citations · 2 across the 2 of their papers we have counts for

collaborators

8 papers

math.SP2004

The semiclassical structure of low-energy states in the presence of a magnetic field

David Borthwick, Alejandro Uribe

We consider a compact Riemannian manifold with a Hermitian line bundle whose curvature is non-degenerate. The Laplacian acting on high tensor powers (the semiclassical regime) of t…

math.DG20032 cited

Selberg's zeta function and the spectral geometry of geometrically finite hyperbolic surfaces

D. Borthwick, C. Judge, P. A. Perry

For hyperbolic Riemann surfaces of finite geometry, we study Selberg's zeta function and its relation to the relative scattering phase and the resonances of the Laplacian. As an ap…

math.DG2001

Determinants of Laplacians and Isopolar Metrics on Surfaces of Infinite Area

D. Borthwick, C. Judge, P. A. Perry

We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, t…

math.SP2001

The spectral density function for the Laplacian on high tensor powers of a line bundle

David Borthwick, Alejandro Uribe

For a symplectic manifold with quantizing line bundle, a choice of almost complex structure determines a Laplacian acting on tensor powers of the bundle. For high tensor powers Gui…

math.SP2000

Scattering theory for conformally compact metrics with variable curvature at infinity

David Borthwick

We develop the scattering theory of general conformally compact metrics. For low frequencies, the domain of the scattering matrix is shown to be frequency dependent. In particular,…

math.SP1999

Scattering poles for asymptotically hyperbolic manifolds

David Borthwick, Peter Perry

For a class of manifolds that includes quotients of real hyperbolic space by a convex co-compact discrete group, we show that the resonances of the meromorphically continued resolv…