Geodesic distance Riesz energy on the sphere
Classical Analysis and ODEs
2016-12-28 v1
Abstract
We study energy integrals and discrete energies on the sphere, in particular, analogs of the Riesz energy with the geodesic distance in place of Euclidean, and observe that the range of exponents for which the uniform distribution optimizes such energies is different from the classical case. We also obtain a general form of the Stolarsky principle, which relates discrete energies to certain discrepancies. This leads to new proofs of discrepancy estimates, as well as the sharp asymptotics of the difference between optimal discrete and continuous energies in the geodesic case.
Cite
@article{arxiv.1612.08442,
title = {Geodesic distance Riesz energy on the sphere},
author = {Dmitriy Bilyk and Feng Dai},
journal= {arXiv preprint arXiv:1612.08442},
year = {2016}
}