Spherical designs via Brouwer fixed point theorem

Abstract

For each N>=c_d*n^{2d*(d+1)/(d+2)} we prove the existence of a spherical n-design on S^d consisting of N points, where c_d is a constant depending only on $d$.

17 pages

References in corpus (1)

• Universally optimal distribution of points on spheres

Cited by in corpus (3)

• Cubature formulas and Sobolev inequalities
• On a spherical code in the space of spherical harmonics
• Small Designs for Path Connected Spaces and Path Connected Homogeneous Spaces