Basic Properties of the Brakke Flow

  • Yoshihiro Tonegawa
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


In this chapter, we present some basic properties satisfied by the Brakke flow.


  1. 7.
    Brakke, K.: The Motion of a Surface by Its Mean Curvature. Mathematical Notes, vol. 20. Princeton University Press, Princeton (1978)Google Scholar
  2. 8.
    Cheeger, J., Haslhofer, R., Naber, A.: Quantitative stratification and the regularity of mean curvature flow. Geom. Funct. Anal.23(3), 828–847 (2013)MathSciNetCrossRefGoogle Scholar
  3. 17.
    Huisken, G.: Asymptotic behavior for singularities of the mean curvature flow. J. Differ. Geom.31(1), 285–299 (1990)MathSciNetCrossRefGoogle Scholar
  4. 19.
    Ilmanen, T.: Elliptic regularization and partial regularity for motion by mean curvature. Mem. Amer. Math. Soc.120, 520 (1994)MathSciNetzbMATHGoogle Scholar
  5. 20.
    Ilmanen, T.: Singularities of mean curvature flow of surfaces (1995).
  6. 39.
    White, B.: Stratification of minimal surfaces, mean curvature flows, and harmonic maps. J. Reine Angew. Math.488, 1–35 (1997)MathSciNetzbMATHGoogle Scholar

Copyright information

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Yoshihiro Tonegawa
    • 1
  1. 1.Tokyo Institute of TechnologyTokyoJapan

Personalised recommendations