On the Fejes Tóth problem about the sum of angles between lines
Authors:
Dmitriy Bilyk and Ryan W. Matzke
Journal:
Proc. Amer. Math. Soc. 147 (2019), 51-59
MSC (2010):
Primary 11K38, 52C35
DOI:
https://doi.org/10.1090/proc/14263
Published electronically:
October 18, 2018
MathSciNet review:
3876730
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Abstract | References | Similar Articles | Additional Information
Abstract: In 1959 Fejes Tóth posed a conjecture that the sum of pairwise nonobtuse 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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Additional Information
Dmitriy Bilyk
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55408
MR Author ID:
757936
Email:
dbilyk@math.umn.edu
Ryan W. Matzke
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55408
MR Author ID:
1115995
Email:
matzk053@umn.edu
Received by editor(s):
January 23, 2018
Published electronically:
October 18, 2018
Additional Notes:
This work is supported by the NSF grant DMS 1665007 (the first author) and the NSF Graduate Research Fellowship 00039202 (the second author)
Communicated by:
Alexander Iosevich
Article copyright:
© Copyright 2018
American Mathematical Society
