Title: Curvature-Torsion Entropy for Twisted Curves under Curve Shortening Flow
\nAuthors: Gabriel Khan
\nCategories: math.DG math.AP
\nComments: 10 pages
\nMSC-class: 53E10 53A04
\n\\\\
\n We study curve-shortening flow for twisted curves in $\\mathbb{R}^3$ (i.e.,
\ncurves with nowhere vanishing curvature $\\kappa$ and torsion $\\tau$) and define
\na notion of torsion-curvature entropy. Using this functional, we show that
\neither the curve develops an inflection point or the eventual singularity is
\nhighly irregular (and likely impossible). In particular, it must be a Type II
\nsingularity which admits sequences along which $\\frac{\\tau}{\\kappa^2} \\to
\n\\infty$. This contrasts strongly with Altschuler’s planarity theorem [J.
\nDifferential Geom. (1991)], which shows that along any essential blow-up
\nsequence, $\\frac{\\tau}{\\kappa} \\to 0$.
\n\\\\ ( https:\/\/arxiv.org\/abs\/2305.07171 , 94kb)<\/p>\n","protected":false},"excerpt":{"rendered":"