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We study the geometric Whitney problem on how a Riemannian manifold $(M,g)$ can be constructed to approximate a metric space $(X,d_X)$.
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Ch. Fefferman, C m C^{m} -extension by linear operators , Ann. of Math. 166
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L. Borcea, V. Druskin, F. Guevara Vasquez, Electrical impedance tomography with resistor networks
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Y. Brudnyi, P. Shvartsman, Whitney’s extension problem for multivariate C 1 , ω C^{1,\omega} functions,
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On the sample complexity of learning smooth cuts on a manifold
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On the sample complexity of testing the manifold hypothesis
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Locally defined principal curves and surfaces
U. Ozertem and D. Erdogmus · 2011
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E. Beretta, M. de Hoop, L. Qiu, Lipschitz Stability of an Inverse Boundary Value Problem for a Schrödinger-Type Equation
2012
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Manifold estimation and singular deconvolution under Hausdorff loss
C. Genovese, M. Perone-Pacifico, I. Verdinelli, L. Wasserman · 2012
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E. Iversen, M. Tygel, B. Ursin, M. de Hoop, Kinematic time migration and demigration of re ections in pre-stack seismic data
2012
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J. Mueller, S. Siltanen, Linear and nonlinear inverse problems with practical applications
2012
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G. Paternain, M. Salo, G. Uhlmann, Tensor Tomography on Simple Surfaces,
2013
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D. Burago, S. Ivanov, Y. Kurylev, A graph discretisation of the Laplace-Beltrami operator , J. Spectr. Theory 4
2014
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Nonparametric ridge estimation
C. Genovese, M. Perone-Pacifico, I- Verdinelli, L. Wasserman, · 2014
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B. Kleiner, J. Lott, Locally collapsed 3-manifolds , Asterisque 365
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Ch. Fefferman, S. Mitter, H. Narayanan, Testing the manifold hypothesis , J. Amer. Math. Soc. 29
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