Critical behavior of collapsing surfaces
Mathematical Physics
2009-08-17 v1 High Energy Physics - Theory
Differential Geometry
math.MP
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.
Cite
@article{arxiv.0903.3369,
title = {Critical behavior of collapsing surfaces},
author = {Kasper Olsen and Christos Sourdis},
journal= {arXiv preprint arXiv:0903.3369},
year = {2009}
}
Comments
23 pages, 10 figures