Convergence for global curve diffusion flows

Abstract

In this note we establish exponentially fast smooth convergence for global curve diffusion flows, and discuss open problems relating embeddedness to global existence (Giga's conjecture) and the shape of Type I singularities (Chou's conjecture).

Keywords

• curve diffusion
• surface diffusion
• global existence
• convergence
• curvature
• partial differential equation
• geometric analysis