Distribution of points on spheres and approximation by zonotopes
Cite this article as: Bourgain, J. & Lindenstrauss, J. Israel J. Math. (1988) 64: 25. doi:10.1007/BF02767366 Abstract
It is proved that if we approximate the Euclidean ball
B n in the Hausdorff distance up to ɛ by a Minkowski sum of N segments, then the smallest possible N is equal (up to a possible logarithmic factor) to c( n) ε −2(. A similar result is proved if n−1)/( n+2) B n is replaced by a general zonoid in R . n References
J. Beck and W. Chen,
Irregularities of Distribution, Cambridge Tracts in Mathematics # 89, 1987.
U. Betke and P. McMullen,
Estimating the sizes of convex bodies from projections
, J. London Math. Soc.
MATH CrossRef MathSciNet Google Scholar
J. Bourgain, J. Lindenstrauss and V. Milman,
Approximation of zonoids by zonotopes, Acta Math. (1988).
T. Figiel, J. Lindenstrauss and V. Milman,
The dimension of almost spherical sections of convex bodies
, Acta Math.
CrossRef MathSciNet Google Scholar
Approximation of a ball by zonotopes using uniform distribution on the sphere, preprint.
V. G. Mazja,
, Springer-Verlag, Berlin, 1985.
MATH Google Scholar