Tag: 渐近性

Title: Curvature-Torsion Entropy for Twisted Curves under Curve Shortening Flow Authors: Gabriel Khan Categories: math.DG math.AP Comments: 10 pages MSC-class: 53E10 53A04 \\ We study curve-shortening flow for twisted curves in $\mathbb{R}^3$ (i.e., curves with nowhere vanishing curvature $\kappa$ and torsion $\tau$) and define a notion of torsion-curvature entropy. Using this functional, we show that either the curve develops an inflection point or the eventual singularity is highly irregular (and likely impossible). In particular, it must be a Type II … Continue reading “Curvature-Torsion Entropy for Twisted Curves under Curve Shortening Flow”