English

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.

Keywords

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

R2 v1 2026-06-21T12:42:25.684Z