Critical behavior of collapsing surfaces

Abstract

We consider the mean curvature evolution of rotationally symmetric surfaces. Using numerical methods, we detect critical behavior at the threshold of singularity formation resembling the one of gravitational collapse. In particular, the mean curvature simulation of a one-parameter family of initial data reveals the existence of a critical initial surface that develops a degenerate neckpinch. The limiting flow of the Type II singularity is accurately modeled by the rotationally symmetric translating soliton.

23 pages, 10 figures

References in corpus (9)

• Critical phenomena in gravitational collapse (Physics Reports)
• A Gradient Flow for Worldsheet Nonlinear Sigma Models
• Integrable Model of Boundary Interaction: The Paperclip
• Dirichlet sigma models and mean curvature flow
• Critical behavior in Ricci flow
• Renormalization group flows and continual Lie algebras
• Mean curvature blow up in mean curvature flow
• Type II extinction profile of maximal solutions to the Ricci flow in ${\mathbb{R}}^2$
• Convex solutions to the mean curvature flow

Cited by in corpus (1)

• Limiting Shapes of Ising Droplets, Ising Fingers, and Ising Solitons