Centro-affine normal flows on curves: Harnack estimates and Ancient solutions

Abstract

We prove that the only compact, origin-symmetric, strictly convex ancient solutions of the planar $p$ centro-affine normal flows are contracting origin-centered ellipses.

arXiv commentI changed the title and fixed some typos. To appear in Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire

Cited by in corpus (3)

• A nonlocal curve flow in centro-affine geometry
• Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds
• Harnack inequalities for evolving hypersurfaces on the sphere