Special Solutions and Global Behaviour

  • Klaus Ecker
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 57)


Definition 2.1 (Mean Curvature Flow) A family of smoothly embedded hypersurfaces (Mt)tI in R n +1 moves by mean curvature if
$$ \frac{{\partial x}} {{\partial t}} = \vec H(x) $$
for xMt and tI, I ⊂ R an open interval. Here \( \vec H(x) \) is the mean curvature vector at xMt.


Curvature Flow Special Solution Global Behaviour Curvature Vector Regularity Theory 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Klaus Ecker
    • 1
  1. 1.Fachbereich für Mathematik und InformatikFreie Universität BerlinBerlinGermany

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