The Curve Shortening Flow in the Metric-Affine Plane

Vladimir Rovenski
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Vladimir Rovenski: Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel

Mathematics, 2020, vol. 8, issue 5, 1-11

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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