Spectral theory and inverse problem on asymptotically hyperbolic orbifolds

Abstract

We consider an inverse problem associated with $n$-dimensional asymptotically hyperbolic orbifolds $(n\ge 2)$ having a finite number of cusps and regular ends. By observing solutions of the Helmholtz equation at the cusp, we introduce a generalized $S$-matrix, and then show that it determines the manifolds with its Riemannian metric and the orbifold structure.

References in corpus (3)

• Wave decay on convex co-compact hyperbolic manifolds
• Inverse Spectral Problems for Collapsing Manifolds I: Uniqueness and Stability
• Conic singularities, generalized scattering matrix, and inverse scattering on asymptotically hyperbolic surfaces

Cited by in corpus (1)

• Inverse scattering on non-compact manifolds with general metric