Conic singularities, generalized scattering matrix, and inverse scattering on asymptotically hyperbolic surfaces
Conic singularities, generalized scattering matrix, and inverse scattering on asymptotically hyperbolic surfaces
Abstract We consider an inverse problem associated with some 2-dimensional non-compact surfaces with conical singularities, cusps and regular ends. Our motivating example is a Riemann surface <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>ℳ</m:mi><m:mo>=</m:mo><m:mrow><m:mi>Γ</m:mi><m:mo>\</m:mo><m:msup><m:mi>ℍ</m:mi><m:mn>2</m:mn></m:msup></m:mrow></m:mrow></m:math> ${\mathcal{M}=\Gamma\backslash\mathbb{H}^{2}}$ associated with a Fuchsian group of the first kind Γ containing parabolic elements. The surface <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>ℳ</m:mi></m:math> ${\mathcal{M}}$ is then non-compact, …