The Curve Shortening Flow in the Metric-Affine Plane

Abstract

We investigated, for the first time, the curve shortening flow in the metric-affine plane and prove that under simple geometric condition (when the curvature of initial curve dominates the torsion term) it shrinks a closed convex curve to a “round point” in finite time. This generalizes the classical result by M. Gage and R.S. Hamilton about convex curves in a Euclidean plane.

Keywords

• curve shortening flow
• affine connection
• curvature
• convex