Fetching the paper…
Reading the bibliography…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc.
Alston S. Householder, The theory of matrices in numerical analysis , Dover Publications, Inc., New York, 1975, Reprint of 1964 edition. MR 0378371 (51 #14539)
1964
Earlier work this paper cites.
R Tyrrell Rockafellar, Convex analysis, volume 28 of princeton mathematics series , 1970
1970
Earlier work this paper cites.
VI Oliker and LD Prussner, On the numerical solution of the equation and its discretizations, i , Numerische Mathematik 54
1989
Earlier work this paper cites.
Luis A. Caffarelli, The regularity of mappings with a convex potential , J. Amer. Math. Soc. 5
1992
Earlier work this paper cites.
Rolf Schneider, Convex bodies: The brunn–minkowski theory , Cambridge University Press, 1993
1993
Earlier work this paper cites.
Wilfrid Gangbo and Robert J. McCann, The geometry of optimal transportation , Acta Math. 177
1996
Earlier work this paper cites.
F. Aurenhammer, F. Hoffmann, and B. Aronov, Minkowski-type theorems and least-squares clustering , Algorithmica 20
1998
Earlier work this paper cites.
Daniel Hug, Generalized curvature measures and singularities of sets with positive reach , Forum Mathematicum 10
1998
Earlier work this paper cites.
Luis A Caffarelli, Sergey A Kochengin, and Vladimir I Oliker, Problem of reflector design with given far-field scattering data , Monge Ampère Equation: Applications to Geometry and Optimization: NSF-CBMS Conference on the Monge Ampère Equation, Applications to Geometry and Optimization, July 9-13, 1997, Florida Atlantic University, vol. 226, American Mathematical Soc., 1999, p. 13
1999
Earlier work this paper cites.
Shmuel Friedland and Reinhard Nabben, On cheeger-type inequalities for weighted graphs , Journal of Graph Theory 41
2002
Earlier work this paper cites.
Gabriel Acosta and Ricardo G Durán, An optimal poincaré inequality in L 1 \mathrm{L}^{1} for convex domains , Proceedings of the American Mathematical Society (2004), 195–202
2004
Earlier work this paper cites.
Grégoire Loeper and Francesca Rapetti, Numerical solution of the monge–ampère equation by a newton’s algorithm , Comptes Rendus Mathematique 340
2005
Cited alongside, same era.
Xi-Nan Ma, Neil S Trudinger, and Xu-Jia Wang, Regularity of potential functions of the optimal transportation problem , Archive for rational mechanics and analysis 177
2005
Cited alongside, same era.
Grégoire Loeper, On the regularity of solutions of optimal transportation problems , Acta mathematica 202
2009
Cited alongside, same era.
Neil S. Trudinger and Xu-Jia Wang, On the second boundary value problem for Monge-Ampère type equations and optimal transportation , Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 8
2009
Cited alongside, same era.
C. Villani, Optimal transport: old and new , Springer Verlag, 2009
Hedy Attouch, Giuseppe Buttazzo, and Gérard Michaille, Variational analysis in sobolev and bv spaces: applications to pdes and optimization , vol. 17, Siam, 2014
2014
Later among the works it cites.
Jean-David Benamou, Brittany D Froese, and Adam M Oberman, Numerical solution of the optimal transportation problem using the monge–ampere equation , Journal of Computational Physics 260
2014
Later among the works it cites.
Pedro Machado Manhaes De Castro, Quentin Mérigot, and Boris Thibert, Intersection of paraboloids and application to minkowski-type problems , Proceedings of the thirtieth annual symposium on Computational geometry, ACM, 2014, p. 308
2014
Later among the works it cites.
Young-Heon Kim and Jun Kitagawa, On the degeneracy of optimal transportation , Communications in Partial Differential Equations 39
2014
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2009
Cited alongside, same era.
Guillaume Carlier, Alfred Galichon, and Filippo Santambrogio, From knothe’s transport to brenier’s map and a continuation method for optimal transport , SIAM Journal on Mathematical Analysis 41
2010
Cited alongside, same era.
Young-Heon Kim and Robert J. McCann, Continuity, curvature, and the general covariance of optimal transportation , J. Eur. Math. Soc. (JEMS) 12
2010
Cited alongside, same era.
by same author, Regularity of optimal maps on the sphere: the quadratic cost and the reflector antenna , Arch. Ration. Mech. Anal. 199
2011
Cited alongside, same era.
Quentin Mérigot, A multiscale approach to optimal transport , Computer Graphics Forum 30
2011
Cited alongside, same era.
Fernando de Goes, Katherine Breeden, Victor Ostromoukhov, and Mathieu Desbrun, Blue noise through optimal transport , ACM Transactions on Graphics (TOG) 31
2012
Cited alongside, same era.
Alessio Figalli, Young-Heon Kim, and Robert J. McCann, Hölder continuity and injectivity of optimal maps , Arch. Ration. Mech. Anal. 209
2013
Cited alongside, same era.
Geograml
Cited in the paper.
Jun Kitagawa, An iterative scheme for solving the optimal transportation problem , Calculus of Variations and Partial Differential Equations 51
2014
Later among the works it cites.
Fernando de Goes, Corentin Wallez, Jin Huang, Dmitry Pavlov, and Mathieu Desbrun, Power particles: an incompressible fluid solver based on power diagrams , ACM Transactions on Graphics (TOG) 34
2015
Later among the works it cites.
Nestor Guillen and Jun Kitagawa, On the local geometry of maps with c-convex potentials , Calc. Var. Partial Differential Equations 52
2015
Later among the works it cites.
Bruno Lévy, A numerical algorithm for L 2 \mathrm{L}^{2} semi-discrete optimal transport in 3d , ESAIM M2AN 49
2015
Later among the works it cites.
2015
Later among the works it cites.
Louis-Philippe Saumier, Martial Agueh, and Boualem Khouider, An efficient numerical algorithm for the l2 optimal transport problem with periodic densities , IMA Journal of Applied Mathematics 80
2015
Later among the works it cites.