Geodesic distance riesz energy on the sphere

Dmitriy Bilyk, Feng Dai

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We study energy integrals and discrete energies on the sphere, in particular, analogues of the Riesz energy with the geodesic distance in place of the Euclidean, and we determine that the range of exponents for which uniform distribution optimizes such energies is different from the classical case. We also obtain a very general form of the Stolarsky principle, which relates discrete energies to certain L2 discrepancies, and prove optimal asymptotic estimates for both objects. This leads to sharp asymptotics of the difference between optimal discrete and continuous energies in the geodesic case, as well as new proofs of discrepancy estimates.

Original languageEnglish (US)
Pages (from-to)3141-3166
Number of pages26
JournalTransactions of the American Mathematical Society
Volume372
Issue number5
DOIs
StatePublished - Sep 1 2019

Bibliographical note

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© 2018 American Mathematical Society.

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