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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…
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…
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,…
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…