A countable set of directions is sufficient for Steiner symmetrization

A countable dense set of directions is sufficient for Steiner symmetrization, but the order of directions matters.

[1]  Philip D. Plowright,et al.  Convexity , 2019, Optimization for Chemical and Biochemical Engineering.

[2]  N. Fusco,et al.  Steiner symmetric extremals in Pólya–Szegö-type inequalities , 2006 .

[3]  Jean Van Schaftingen Universal approximation of symmetrizations by polarizations , 2005, Proceedings of the American Mathematical Society.

[4]  A. Burchard Steiner Symmetrization is Continuous in W1,p , 1997 .

[5]  R. Schneider Convex Bodies: The Brunn–Minkowski Theory: Minkowski addition , 1993 .

[6]  Franz E Schuster,et al.  General $L_p$ affine isoperimetric inequalities , 2008, 0809.1983.

[7]  An isoperimetric inequality for convex polygons and convex sets with the same symmetrals , 1986 .

[8]  J. Steiner,et al.  Einfache Beweise der isoperimetrischen Hauptsätze. , 1838 .

[9]  A Result on the Steiner Symmetrization of a Compact Set , 1976 .

[10]  T. Apostol Introduction to analytic number theory , 1976 .

[11]  E. T. An Introduction to the Theory of Numbers , 1946, Nature.

[12]  Jean Bourgain,et al.  Estimates related to steiner symmetrizations , 1989 .

[13]  J. Alonso,et al.  Convex and Discrete Geometry , 2009 .

[14]  Jean Van Schaftingen Approximation of symmetrizations and symmetry of critical points , 2006 .

[15]  Jörg M. Wills,et al.  Handbook of Convex Geometry , 1993 .

[16]  G. Bianchi,et al.  Steiner symmetrals and their distance from a ball , 2003 .

[17]  Erwin Lutwak,et al.  Orlicz projection bodies , 2010 .

[18]  V. Milman,et al.  Rapid Steiner Symmetrization of Most of a Convex Body and the Slicing Problem , 2005, Combinatorics, Probability and Computing.

[19]  P. R. Scott Planar Rectangular Sets and Steiner Symmetrization , 1998 .

[20]  V. V. Buldygin,et al.  Brunn-Minkowski inequality , 2000 .

[21]  V. Milman,et al.  Isomorphic Steiner symmetrization , 2003 .

[22]  The perimeter inequality under Steiner symmetrization: Cases of equality , 2005 .

[23]  G. Talenti The Standard Isoperimetric Theorem , 1993 .

[24]  A. McNabb Partial Steiner symmetrization and some conduction problems , 1967 .

[25]  R. Gardner Symmetrals and X-rays of planar convex bodies , 1983 .

[26]  R. Gardner Geometric Tomography: Parallel X-rays of planar convex bodies , 2006 .