RECENT PUBLICATIONS OF VLADIMIR OLIKER

    BOOKS

  1. Geometric Analysis, Mathematical Relativity, and Nonlinear Partial Differential Equations, M. Ghomi, J. Li, J. McCuan, V. Oliker, F. Schwartz, G. Weinstein (eds.), Contemporary Mathematics, vol. 599, AMS, 2013, 1-243

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  1. Mathematical aspects of design of beam shaping surfaces in geometrical optics, in Trends in Nonlinear Analysis, ed. by M. Kirkilionis, S. Kromker, R. Rannacher, F. Tomi, Springer-Verlag, 2003, pp. 193-224. [pdf].
  2. Computational algorithms for constructing reflectors (with S. Kochengin), Computing and Visualization in Science, 6:15-21(2003),
  3. Optical design of single reflector systems and the Monge-Kantorovich mass transfer problem (with T. Glimm), J. of Math. Sciences, Vol. 117, No. 3(2003), 4096-4108. [pdf].
  4. Optical design of two-reflector systems, the Monge-Kantorovich mass transfer problem and Fermat's principle (with T. Glimm), Indiana Univ.  Math. J., Vol. 53, No. 5(2004), 1255-1277. [pdf].
  5. Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties, Proceedings of SPIE, Nonimaging Optics and Efficient Ellimination Systems, ed. by R. Winston and R.J. Koshel, v. 5942(2005), 594207-1 - 594207-12.
  6. Optical design of two-mirror beam-shaping systems. Convex and non-convex solutions for symmetric and non-symmetric data, Proceedings of SPIE, Laser Beam Shaping VI - Optical Engineering and Instrumentation, ed. by F. M. Dickey and D. L. Shealy, v. 5876(2005), 203-214.
  7. A variational solution of A.D. Aleksandrov problem of existence of a noncompact complete convex polytope with prescribed integral Gauss curvature, Banach Center Publications, v. 69(2005), 81-90. [pdf].
  8. A rigorous method for synthesis of offset shaped reflector antennas, Computing Letters, vol. 2, No. 1-2(2006), 29-49. [pdf].
  9. Freeform optical systems with prescribed irradiance properties in the near-field, Proceedings of SPIE, International Optical Design Conference 2006, ed. by G.G. Gregory, J.M. Howard and R.J. Koshel, v. 6342(2006), 634211-1 - 634211-12.
  10. Existence of optimal maps in the reflector-type problems (with W. Gangbo), ESAIM. Control, Optimization and Calculus of Variations, Vol. 13, No.1(2007), 93-106.[pdf].
  11. Uniqueness of starshaped compact hypersurfaces with prescribed m-th mean curvature in hyperbolic space (with J.L. Barbosa and J.H. Lira), Illinois J. of Mathematics, Vol. 51, No.2 (2007), 571-582. [pdf].
  12. Embedding $S^n$ into $R^{n+1}$ with prescribed integral Gauss curvature and optimal mass transport on $S^n$, Advances in Mathematics, Vol. 213(2007), 600-620. [pdf].
  13. Optical design of freeform two-mirror beam-shaping systems, J. of Optical Society of America A, 24(12):3741-3752, 2007.
  14. A Minkowski-style theorem for focal functions of compact convex reflectors, Transactions of the AMS, 360 (2008), no. 2, 563-574. [pdf].
  15. On the geometry of convex reflectors, II. Polar reflectors, Results in Math., no. 52 (2008), 359-367.
  16. Weak solutions of one inverse problem in geometric optics (with L. Caffarelli), J. of Math. Sciences, Vol. 154(1)(2008), 37-46, 2008.
  17. On design of freeform refractive beam-shapers, sensitivity to figure error and convexity of lenses, J. of Optical Society of America A, 25(12)(2008), 3067-3076.
  18. A characterization of revolution quadrics by a system of partial differential equations, Proceedings of the AMS, 138(2010), no. 11, 4075-4080.
  19. Kummer configurations and $S_m$-reflector problems:Hypersurfaces in ${\mathbb{R}^{n+1}}$ with given mean intensity, Results in Math., 56(2009), 519-535.
  20. Sensitivity to figure error of a freeform refractive beam shaper, Proceedings of SPIE, Nonimaging Optics:VI Conference, ed. by R. Winston and J. Gordon, vol. 7423(2009), 04-1--04-10.
  21. Designing freeform lenses for intensity and phase control of coherent light with help from geometry and mass transport, Archive for Rational Mechanics and Analysis, 201(2011), 1013-1045.
  22. An optimal mass transport approach to the near-field reflector problem in optical design (with T. Graf), Inverse Problems, 28(2012), 1-15.
  23. Ray mapping and illumination control (with J. Rubinstein and G. Wolansky),Journal of Photonics for Energy, 3(1)(2013), 035599-1--7.
  24. Differential equations for design of a freeform single lens with prescribed irradiance properties. Optical Engineering, 53(3)(2014), 031302-1--10.
  25. Controlling light with freeform optics: recent progress in computational methods for optical design of freeform lenses with prescribed irradiance properties (with B. Cherkasskiy), Proc. SPIE 9191(2014), 919105-1--919105-7
  26. Controlling light with freeform optics, SPIE Newsroom. DOI:10.1117/2.1201009.001234. Published Online: September 21, 2014. http://spie.org/x110544.xml, 4 pages.
  27. On the use of the supporting quadric method in the problem of the light field eikonal calculation, (with L. Doskolovich, M. Moiseev, E. Bezus), Optics Express, 23(2015), 19605-19617.
  28. Diffraction effects in freeform optics (with M. Ricketts and R. Winston), Proc. SPIE 9572(2015), doi:10.1117/12.2191895.
  29. Supporting quadric method in optical design of freeform lenses for illumination control of a collimated light, (with J. Rubinstein and G. Wolansky), Advances in Appl. Math., 62(2015), 160-183.
  30. Freeform multifocal lenses designed with the SQM: geometry and diffraction. In R. Winston and J. Gordon (Ed.), Proc. SPIE, Vol. 9955(2016), Nonimaging Optics: doi:10.1117/12.2238025 (pp. 995501-995508).
  31. Controlling light with freeform multifocal lens designed with supporting quadric method(SQM), Optics Express, 25(4)(2017), A59 - A72.