Monotonicity of the modulus under curve shortening flow

2024/09/04 by Arjun Sobnack, Sobnack, Arjun, Peter M. Topping +1
Chemical Engineering · Engineering · #Rheology and Fluid Dynamics Studies #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2409.03098

Abstract

Given two disjoint nested embedded closed curves in the plane, both evolving under curve shortening flow, we show that the modulus of the enclosed annulus is monotonically increasing in time. An analogous result holds within any ambient surface satisfying a lower curvature bound.

Related

• A short proof of monotonicity formula for curve shortening flow in 3D
• Stabilization technique applied to curve shortening flow in the plane
• Curve shortening flow with an ambient force field
• Curvature bound for curve shortening flow via distance comparison and a direct proof of Grayson's theorem
• A comparison theorem for the isoperimetric profile under curve shortening flow