Open AccessMinimal surface generating flow for space curves of non-vanishing torsion
Author(s) -
Jiří Minarčík,
Michal Beneš
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2022011
Subject(s) - mathematics , torsion (gastropod) , curvature , mean curvature flow , geometry , torsion of a curve , surface (topology) , flow (mathematics) , minimal surface , mathematical analysis , mean curvature , medicine , surgery
This article introduces new geometric flow for space curves with positive curvature and torsion. Curves evolving according to this motion law trace out a zero mean curvature surface. First, the geometry of surfaces defined as trajectories of moving curves is analyzed and the minimal surface generating flow is derived. Then, an upper bound for the area of the generated minimal surface and for the terminating time of the flow is provided.