Articles by Prof. Shlomo Reisner

Updated April 2019

  1. M. Meyer and S. Reisner, Ellipsoids are the only local maximizers of the volume product. Mathematika 65 (2019), 500--504. arXiv 1812.11607.
  2. M. Meyer and S. Reisner, The isotropy constant and boundary properties of convex bodies. Proceedings of the American Mathematical Society 144 (2016), no.9, 3935--3947.
  3. K. J. Boroczky, E. Makai Jr., M. Meyer and S. Reisner, On the volume product of planar polar convex bodies Lower estimates with stability. Studia Sci. Math. Hungar. 50 (2013), 159--198.
  4. S. Reisner, C. Schuett and E. M. Werner, Mahler's conjecture and curvature. International Math. Research Notices, vol. 2012 (2012), 1--16.
  5. M. Meyer and S. Reisner, The convex intersection body of a convex body. Glasgow Math. J. 53 (2011), 523--534.
  6. Y. Gordon, M. Junge, M. Meyer and S. Reisner, The GL-l.u.st. constant and asymmetry of the Kalton-Peck twisted sum in finite dimensions, Proceedings of the American Math. Soc. 139 (2011), 2793--2805.
  7. M. Meyer and S. Reisner, On the volume product of polygons. Abhandlungen aus dem Mathematischen Seminar der Universitaet Hamburg 81 (2011), 93--100.

  8. J. Kim and S. Reisner, Local minimality of the volume-product at the simplex. Mathematika 57 (2011), 121--134.
  9. M. Fradelizi, Y. Gordon, M. Meyer and S. Reisner, The case of equality for an inverse Santal\'o functional inequality, Advances in Geometry 10 (2010), 621--630.
  10. M. A. Lopez and S. Reisner, Hausdorff approximation of 3D convex polytopes, Information Processing Letters 107 (2008) 76--82.
  11. M. Meyer and S. Reisner, Shadow systems and volumes of polar convex bodies, Mathematika 53 (2006), 129--148.
  12. M. A. Lopez and S. Reisner, Hausdorff approximation of convex polygons, Computational Geometry, Theory and Applications 32 (2005), 139--158.
  13. S. Reisner, A note on a theorem of Borwein, Borwein, Fee and Girgensohn, Mathematical Inequalities and Applications 5 (2002), 753--754.
  14. M. A. Lopez and S. Reisner, Linear time approximation of 3D polytopes, Computational Geometry, Theory and Applications 23 (2002), 291--301.
  15. Y. Gordon, V. Maiorov, M. Meyer and S. Reisner, On best approximation by ridge functions in the uniform norm, Constructive Approximation 18 (2002), 61--85.
  16. S. Reisner, C. Schuett and E. Werner, Dropping a vertex or a facet from a convex polytope, Forum Mathematicum 13 (2001), 359--378.
  17. M. A. Lopez and S. Reisner, Efficient approximation of convex polygons, International J. of Computational Geometry and Applications 10 (2000), 445--452.
  18. M. Meyer and S. Reisner, A geometric proof of some inequalities involving mixed volumes, Beitraege zur Algebra und Geometrie 41 (2000), 335--344.
  19. M. A. Lopez and S. Reisner, Algorithms for polyhedral approximation of multidimensional ellipsoids, J. of Algorithms 33 (1999), 140--165.
  20. M. A. Lopez and S. Reisner, A special case of Mahler's conjecture, Discrete and Computational Geometry 20 (1998), 219--227.
  21. M. Meyer and S. Reisner, Inequalities involving integrals of polar - conjugate concave functions, Monatshefte fuer Math. 125 (1998), 219--227.
  22. Y. Gordon, S. Reisner and C. Schuett, Umbrellas and polytopal approximation of the Euclidean ball, J. of Approximation Theory 90 (1997), 9--22.
  23. Y. Gordon, M. Meyer and S. Reisner, Constructing a polytope to approximate a convex body, Geometriae Dedicata 57 (1995), 217--222.
  24. S. Reisner, Operators factoring through Banach lattices and ideal norms, Serdica Math. J. 21 (1995), 75--89.
  25. Y. Gordon, M. Meyer and S. Reisner, Volume approximation of convex bodies by polytopes - a constructive method, Studia Mathematica (1994), 81--95.
  26. S. Reisner, Some remarks on Lozanovskii's intermediate normed lattices, Bull. Polish Ac. Sci., Mathematics, 41 (1993), 189--196.
  27. M. Meyer, S. Reisner and M. Schmuckenschlaeger, The volume of the intersection of a convex body with its translates, Mathematika 40 (1993), 278--289.
  28. M. Meyer and S. Reisner, Characterization of affinely--rotation-- invariant log--concave measures by section--centroid location, Geometrical Aspects of Functional Analysis, LNM 1469 (1991), 145--152, Springer-Verlag.
  29. M. Meyer and S. Reisner, A geometric property of the boundary of symmetric convex bodies and convexity of flotation surfaces, Geometriae Dedicata 37 (1991), 327--337.
  30. S. Reisner, Certain Banach spaces associated with graphs and CL-spaces with 1-unconditional bases, Journal of the London Math. Soc. 43 (1991), 137--148.
  31. M. Meyer and S. Reisner, Charactrization of ellipsoids by section--centroid location, Geometriae Dedicata (1989), 345-355.
  32. Y. Gordon, M. Meyer and S. Reisner, Zonoids with minimal volume--product - a new proof, Proceedings of the American Math. Soc. 104 (1988), 273--276.
  33. S. Reisner, On two theorems of Lozanovskii concerning intermediate Banach lattices, Geometrical Aspects of Functional Analysis, LNM 1317 (1988), 67--83, Springer-Verlag.
  34. S. Reisner, Minimal volume product in Banach spaces with a 1-unconditional basis, Journal of the London Math. Soc. 36 (1987), 126--136.
  35. S. Reisner, Zonoids with minimal volume--product, Math. Zeitschrift 192 (1986), 339--346.
  36. S. Reisner, Random Polytopes and the volume--product of symmetric convex bodies, Math. Scandinavica 57 (1985), 386--392.
  37. S. Reisner, Product of volumes of unit balls, Longhorn Notes, The University of Texas, 1983-1984, 193--202.
  38. Y. Gordon and S. Reisner, Some aspects of volume estimates to various parameters in Banach spaces theory, Proceedings of Research Workshop on Banach Spaces Theory, University of Iowa, June 29 - July 31, 1981. Edited by Bor-Lou Lin, University of Iowa Press, 23--53.
  39. Y. Gordon and S. Reisner, Some geometrical properties of Banach spaces of polynomials, Israel Journal of Math. 42 (1982), 99--116.
  40. M. Cwikel and S. Reisner, Interpolation of uniformly convex Banach spaces, Proceedings of the American Math. Soc. 84 (1982), 555--559.
  41. S. Reisner, On the duals of Lorentz function and sequence spaces, Indiana University Journal of Math. 31 (1982), 65--72.
  42. S. Reisner, A factorization theorem in Banach lattices and its application to Lorentz spaces, Annales de l'Institute Fourier 31 (1981), 239--255.
  43. S. Reisner, Operators which factor through convex Banach lattices, Canadian Journal of Math. 32 (1980), 1482--1500.
  44. S. Reisner, On Banach spaces having the property G.L., Pacific Journal of Math. 83 (1979), 505--521.