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Given only a collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to solve elliptic partial differential equations (PDEs) supplemented with boundary conditions.
Extension of the rauch comparison theorem to submanifolds
FW Warner · 1966
Earlier work this paper cites.
Continuity properties of the injectivity radius function
Paul E Ehrlich · 1974
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Geometric curvature bounds in riemannian manifolds with boundary
Stephanie B Alexander, I David Berg, and Richard L Bishop · 1993
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Simple boundary correction for kernel density estimation
M.C. Jones · 1993
Earlier work this paper cites.
A simple nonnegative boundary correction method for kernel density estimation
MC Jones and PJ Foster · 1996
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An improved estimator of the density function at the boundary
M. C. Jones S. Zhang, R. J. Karunamuni · 1999
Earlier work this paper cites.
Probability density function estimation using gamma kernels
SongXi Chen · 2000
Earlier work this paper cites.
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Mikhail Belkin and Partha Niyogi · 2003
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On boundary correction in kernel density estimation
Rhoana J Karunamuni and Tom Alberts · 2005
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Kernel density estimation on Riemannian manifolds
Bruno Pelletier · 2005
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Convergence of graph laplacians on random neighborhood graphs
M Hein, JY Audibert, and U von Luxburg · 2007
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Chernoff’s theorem and discrete time approximations of brownian motion on manifolds
Oleg G Smolyanov, Heinrich v Weizsäcker, and Olaf Wittich · 2007
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Submanifold density estimation
Arkadas Ozakin and Alexander G Gray · 2009
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Vector diffusion maps and the connection laplacian
Density estimation on manifolds with boundary
Tyrus Berry and Timothy Sauer · 2017
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The matlab radial basis function toolbox
S. A. Sarra · 2017
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Introduction to Riemannian Manifolds
John Lee · 2018
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When locally linear embedding hits boundary, 2018
Hau tieng Wu and Nan Wu · 2018
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Alexandrov geometry: preliminary version no. 1, 2019
Stephanie Alexander, Vitali Kapovitch, and Anton Petrunin · 2019
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Consistent manifold representation for topological data analysis
Tyrus Berry and Timothy Sauer · 2019
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Yoon Tae Kim and Hyun Suk Park · 2013
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Nonparametric kernel density estimation near the boundary
Peter Malec and Melanie Schienle · 2014
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