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Abstract We show that in Euclidean 3‐space any closed curve which contains the unit sphere within its convex hull has length , and characterize the case of equality. This result generalizes the authors' recent solution to a conjecture of Zalgaller. Furthermore, for the analogous problem in dimensions, we include the estimate by Nazarov, which is sharp up to the constant .
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Sums of transcendental dilates
Abstract We show that there is an absolute constant such that for any finite subset of and any transcendental number . By a construction of Konyagin and Łaba, this is best possible up to the constant .
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- Award ID(s):
- 2054452
- PAR ID:
- 10421305
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Bulletin of the London Mathematical Society
- ISSN:
- 0024-6093
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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