The harmonic mean curvature flow of nonconvex surfaces in ℝ3

Panagiota Daskalopoulos, Natasa Sesum

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We consider a compact star-shaped mean convex hypersurface. We prove that in some cases the flow exists until it shrinks to a point. We also prove that in the case of a surface of revolution which is star-shaped and mean convex, a smooth solution always exists up to some finite time T < ∞ at which the flow shrinks to a point asymptotically spherically.

Original languageEnglish (US)
Pages (from-to)187-215
Number of pages29
JournalCalculus of Variations and Partial Differential Equations
Volume37
Issue number1
DOIs
StatePublished - Nov 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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