The Journal of Geometric Analysis

, Volume 5, Issue 3, pp 293–358

Mean curvature flow through singularities for surfaces of rotation

  • Steven Altschuler
  • Sigurd B. Angenent
  • Yoshikazu Giga
Article

Abstract

In this paper, we study generalized “viscosity” solutions of the mean curvature evolution which were introduced by Chen, Giga, and Goto and by Evans and Spruck. We devote much of our attention to solutions whose initial value is a compact, smooth, rotationally symmetric hypersurface given by rotating a graph around an axis. Our main result is the regularity of the solution except at isolated points in spacetime and estimates on the number of such points.

Math Subject Classification

58G11 35K55 

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Copyright information

© Mathematica Josephina, Inc. 1995

Authors and Affiliations

  • Steven Altschuler
    • 1
    • 2
    • 3
  • Sigurd B. Angenent
    • 1
    • 2
    • 3
  • Yoshikazu Giga
    • 1
    • 2
    • 3
  1. 1.Centre for Mathematics and its ApplicationsAustralian National UniversityCanberraAustralia
  2. 2.Department of Mathematics, Van Vleck HallUniversity of Wisconsin at MadisonMadisonUSA
  3. 3.Department of MathematicsHokkaido UniversitySapporoJapan

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