Free Access
Volume 13, Number 1, January-March 2007
Page(s) 93 - 106
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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.