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On the Fejes T\'oth Problem about the Sum of Angles Between Lines

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arxiv 1801.07837 v1 pith:X7AB2DDD submitted 2018-01-24 math.MG math.CA

Dmitriy Bilyk , Ryan W Matzke This is my paper · ORCID
classification math.MGmath.CA
keywords anglesconjecturefejesapproachesbasisboundscasecorresponding
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abstract

In 1959 Fejes T\'oth posed a conjecture that the sum of pairwise non-obtuse angles between $N$ unit vectors in $\mathbb S^d$ is maximized by periodically repeated elements of the standard orthonormal basis. We obtain new improved upper bounds for this sum, as well as for the corresponding energy integral. We also provide several new approaches to the only settled case of the conjecture: $d=1$.

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  1. Energy on spheres and discreteness of minimizing measures

    math.CA 2019-08 conditional novelty 7.0 of 10

    For non-even p, every minimizer of the p-frame energy on the sphere has support with empty interior, and for potentials with finitely many positive Gegenbauer coefficients a discrete minimizer always exists.

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