A translation of Zalgaller's "The shortest space curve of unit width" (1994)

Abstract

This is an English translation of V. A. Zalgaller's article "On a problem of the shortest space curve of unit width" that appeared in $Matematicheskaya\ Fizika,\ Analiz,\ Geometriya$ v. 1 (1994) n. 3--4, 454--461. We refer interested readers to Ghomi (2018) for up-to-date discussion; the curve $L_{3}$ of length 3.9215... in Zalgaller (1994) still appears to be shortest, whereas the closed curve $L_{5}$ is provably not of unit width. I am thankful to Natalya Pluzhnikov for her dedicated work and to the B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine for permission to post this translation on the arXiv.