Critical behavior of collapsing surfaces

Publication: Research - peer-reviewJournal article – Annual report year: 2009

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We consider the mean curvature evolution of rotationally symmetric surfaces. Using numerical methods, we detect critical behavior at the threshold of singularity formation resembling that 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.
Original languageEnglish
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number35
ISSN1751-8113
DOIs
StatePublished - 2009
Peer-reviewedYes
CitationsWeb of Science® Times Cited: 1
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