Mean curvature flow closes open ends of noncompact surfaces of rotation

Yoshikazu Giga, Yukihiro Seki, Noriaki Umeda

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5 Citations (Scopus)

Abstract

We discuss the motion of noncompact axisymmetric hypersurfaces Γt evolved by mean curvature flow. Our study provides a class of hypersurfaces that share the same quenching time with the shrinking cylinder evolved by the flow and prove that they tend to a smooth hypersurface having no pinching neck and having closed ends at infinity of the axis of rotation as the quenching time is approached. Moreover, they are completely characterized by a condition on initial hypersurface.

Original languageEnglish
Pages (from-to)1508-1529
Number of pages22
JournalCommunications in Partial Differential Equations
Volume34
Issue number11
DOIs
Publication statusPublished - Jan 1 2009

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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