Given a hyperbolic surface with geodesic boundary S, the lengths of a maximal system of disjoint simple geodesic arcs on S
that start and end at @S perpendicularly are coordinates on the Teichm¨uller space T (S). We express the Weil-Petersson Poisson
structure of T (S) in this system of coordinates, and we prove that it limits pointwise to the piecewise-linear Poisson structure
defined by Kontsevich on the arc complex of S. At the same time, we obtain a formula for the first-order variation of the distance between two closed geodesics under Fenchel-Nielsen deformation.
We prove that if a complete, properly embedded, finite-topology minimal surface in S2×R contains a line, then its ends are asymptotic to helicoids, and that if the surface is an annulus, it must be a helicoid.
Paternain G P, Salo M, Uhlmann G, et al. Tensor tomography on surfaces[J]. Inventiones Mathematicae, 2011, 193(1): 229-247.
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Gabriel P Paternain · Mikko Salo · Gunther Uhlmann. Tensor tomography: progress and challenges. 2013.
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Gabriel P Paternain · Mikko Salo · Gunther Uhlmann. The attenuated ray transform for connections and Higgs fields. 2011.
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Paternain G P, Salo M, Uhlmann G, et al. On the Range of the Attenuated Ray Transform for Unitary Connections[J]. International Mathematics Research Notices, 2013, 2015(4): 873-897.
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David Dos Santos Ferreira · Carlos E Kenig · Mikko Salo. Determining an Unbounded Potential from Cauchy Data in Admissible Geometries. 2011.
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Paternain G P, Salo M, Uhlmann G, et al. Invariant distributions, Beurling transforms and tensor tomography in higher dimensions[J]. Mathematische Annalen, 2014: 305-362.
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Gareth Ainsworth. The Attenuated Magnetic Ray Transform on Surfaces. 2012.
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Fiorini R A. How Random is Your Tomographic Noise? A Number Theoretic Transform (NTT) Approach[J]. Fundamenta Informaticae, 2014: 135-170.
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Guillarmou C. Lens rigidity for manifolds with hyperbolic trapped set[J]. Journal of the American Mathematical Society, 2014.
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Caro P, Salo M. Stability of the Calder\\\u0027on problem in admissible geometries[J]. Inverse Problems and Imaging, 2014, 8(4): 939-957.
We show that the attenuated geodesic ray transform on two dimensional simple surfaces is injective. Moreover, we give a stability estimate and develop a reconstruction procedure.