Homology, Homotopy and Applications

Volume 24 (2022)

Number 2

Nondegenerate homotopy and geometric flows

Pages: 255 – 264

DOI: https://dx.doi.org/10.4310/HHA.2022.v24.n2.a12

Authors

Jiří Minarčík (Department of Mathematics, FNSPE, Czech Technical University in Prague, Czech Republic)

Michal Beneš (Department of Mathematics, FNSPE, Czech Technical University in Prague, Czech Republic)

Abstract

Formulating geometric flows of space curves using quantities derived from the Frenet frame restricts the motion to one connected component of the space of locally convex curves. A new invariant quantity called tangent turning sign is proposed to determine the nondegenerate homotopy type of the initial curve and identify its possible shapes during the geometric flow.

Keywords

locally convex curve, geometric flow, nondegenerate homotopy

2010 Mathematics Subject Classification

14H50, 53C44, 55P15

Full Text (PDF format)

This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic under the OP RDE grant number CZ.02.1.01/0.0/0.0/16 019/0000753 “Research centre for lowcarbon energy technologies”.

Received 5 October 2021

Received revised 12 November 2021

Accepted 17 November 2021

Published 24 August 2022