On the evolution of convex hypersurfaces by the Qk flow

M. Cristina Caputo, Panagiota Daskalopoulos, Natasa Sesum

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We prove the existence and uniqueness of a C1,1 solution of the Qk flow in the viscosity sense for compact convex hypersurfaces σt embedded in Rn+1 (n ≥ 2). The solution exists up to the time T < ∞ at which the enclosed volume becomes zero. In particular, for compact convex hypersurfaces with flat sides we show that, under a certain non-degeneracy initial condition, the interface separating the flat from the strictly convex side, becomes smooth, and it moves by the Qk-1 flow at least for a short time.

Original languageEnglish (US)
Pages (from-to)415-442
Number of pages28
JournalCommunications in Partial Differential Equations
Volume35
Issue number3
DOIs
StatePublished - Mar 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • Curvature flows
  • Weakly convex

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