Free Access
Issue
ESAIM: COCV
Volume 13, Number 1, January-March 2007
Page(s) 93 - 106
DOI https://doi.org/10.1051/cocv:2006017
Published online 14 February 2007
  1. T. Abdellaoui and H. Heinich, Sur la distance de deux lois dans le cas vectoriel. C.R. Acad. Sci. Paris Sér. I Math. 319 (1994) 397–400. [Google Scholar]
  2. N. Ahmad, The geometry of shape recognition via the Monge-Kantorovich optimal transport problem. Ph.D. dissertation (2004). [Google Scholar]
  3. L.A. Caffarelli and V.I. Oliker, Weak solutions of one inverse problem in geometric optics. Preprint (1994). [Google Scholar]
  4. L.A. Caffarelli and S. Kochengin and V.I. Oliker, On the numerical solution of the problem of reflector design with given far-field scattering data. Cont. Math. 226 (1999) 13–32. [Google Scholar]
  5. W. Gangbo, Quelques problèmes d'analyse non convexe. Habilitation à diriger des recherches en mathématiques. Université de Metz (Janvier 1995). [Google Scholar]
  6. W. Gangbo and R.J. McCann, The geometry of optimal transportation. Acta Math. 177 (1996) 113–161. [CrossRef] [MathSciNet] [Google Scholar]
  7. W. Gangbo and R. McCann, Shape recognition via Wasserstein distance. Quart. Appl. Math. 58 (2000) 705–737. [CrossRef] [MathSciNet] [Google Scholar]
  8. T. Glimm and V.I. Oliker, Optical design of single reflector systems and the Monge-Kantorovich mass transfer problem. J. Math. Sci. 117 (2003) 4096–4108. [CrossRef] [MathSciNet] [Google Scholar]
  9. T. Glimm and V.I. Oliker, Optical design of two-reflector systems, the Monge-Kantorovich mass transfer problem and Fermat's principle. Indiana Univ. Math. J. 53 (2004) 1255–1278. [CrossRef] [MathSciNet] [Google Scholar]
  10. Pengfei Guan and Xu-Jia Wang, On a Monge-Ampère equation arising in geometric optics J. Differential Geometry 48 (1998) 205–223. [Google Scholar]
  11. H.G. Kellerer, Duality theorems for marginal problems. Z. Wahrsch. Verw. Gebiete 67 (1984) 399–432. [Google Scholar]
  12. B.E. Kinber, On two reflector antennas. Radio Eng. Electron. Phys. 7 (1962) 973–979. [Google Scholar]
  13. M. Knott and C.S. Smith, On the optimal mapping of distributions. J. Optim. Theory Appl. 43 (1984) 39–49. [CrossRef] [MathSciNet] [Google Scholar]
  14. E. Newman and V.I. Oliker, Differential-geometric methods in design of reflector antennas. Symposia Mathematica 35 (1994) 205–223. [Google Scholar]
  15. A.P. Norris and B.S. Westcott, Computation of reflector surfaces for bivariate beamshaping in the elliptic case. J. Phys. A: Math. Gen 9 (1976) 2159–2169. [CrossRef] [Google Scholar]
  16. V.I. Oliker and P. Waltman, Radially symmetric solutions of a Monge-Ampere equation arising in a reflector mapping problem. Proc. UAB Int. Conf. on Diff. Equations and Math. Physics, edited by I. Knowles and Y. Saito, Springer. Lect. Notes Math. 1285 (1987) 361–374. [CrossRef] [Google Scholar]
  17. V.I. Oliker, On the geometry of convex reflectors. PDE's, Submanifolds and Affine Differential Geometry, Banach Center Publications 57 (2002) 155–169. [Google Scholar]
  18. R.T. Rockafellar, Convex Analysis. Princeton University Press, Princeton (1970). [Google Scholar]
  19. L. Rüschendorf, On c-optimal random variables. Appl. Stati. Probab. Lett. 27 (1996) 267–270. [Google Scholar]
  20. C. Smith and M. Knott, On Hoeffding-Fréchet bounds and cyclic monotone relations. J. Multivariate Anal. 40 (1992) 328–334. [CrossRef] [MathSciNet] [Google Scholar]
  21. X.-J. Wang, On design of a reflector antenna. Inverse Problems 12 (1996) 351–375. [Google Scholar]
  22. X.-J. Wang, On design of a reflector antenna II. Calculus of Variations and PDE's 20 (2004) 329–341. [CrossRef] [Google Scholar]
  23. B.S. Westcott, Shaped Reflector Antenna Design. Research Studies Press, Letchworth, UK (1983). [Google Scholar]
  24. S.T. Yau, Open problems in geometry, in Differential Geometry. Part 1: Partial Differential Equations on Manifolds (Los Angeles, 1990), R. Greene and S.T. Yau Eds., Proc. Sympos. Pure Math., Amer. Math. Soc. 54 (1993) 1–28. [Google Scholar]

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