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The Curve Shortening Flow in the Metric-Affine Plane

Author

Listed:
  • Vladimir Rovenski

    (Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel)

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.

Suggested Citation

  • Vladimir Rovenski, 2020. "The Curve Shortening Flow in the Metric-Affine Plane," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:701-:d:353284
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