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- W2963972110 abstract "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> ${mathcal{M}=Gammabackslashmathbb{H}^{2}}$ 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, and has a finite number of cusps and elliptic singular points, which is regarded as a hyperbolic orbifold. We introduce a class of Riemannian surfaces with conical singularities on its finite part, having cusps and regular ends at infinity, whose metric is asymptotically hyperbolic. By observing solutions of the Helmholtz equation at the cusp, we define a generalized S-matrix. We then show that this generalized S-matrix determines the Riemannian metric and the structure of conical singularities." @default.
- W2963972110 created "2019-07-30" @default.
- W2963972110 creator A5052627284 @default.
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- W2963972110 date "2014-09-27" @default.
- W2963972110 modified "2023-09-29" @default.
- W2963972110 title "Conic singularities, generalized scattering matrix, and inverse scattering on asymptotically hyperbolic surfaces" @default.
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- W2963972110 doi "https://doi.org/10.1515/crelle-2014-0076" @default.
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