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Mean curvature flow through singularities for surfaces of rotation

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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.

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Authors and Affiliations

  1. Centre for Mathematics and its Applications, Australian National University, GPO Box 4, ACT-2601, Canberra, Australia

    Steven Altschuler, Sigurd B. Angenent & Yoshikazu Giga

  2. Department of Mathematics, Van Vleck Hall, University of Wisconsin at Madison, 53706, Madison, Wisconsin, USA

    Steven Altschuler, Sigurd B. Angenent & Yoshikazu Giga

  3. Department of Mathematics, Hokkaido University, 060, Sapporo, Japan

    Steven Altschuler, Sigurd B. Angenent & Yoshikazu Giga

Authors
  1. Steven Altschuler
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  2. Sigurd B. Angenent
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  3. Yoshikazu Giga
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Altschuler, S., Angenent, S.B. & Giga, Y. Mean curvature flow through singularities for surfaces of rotation. J Geom Anal 5, 293–358 (1995). https://doi.org/10.1007/BF02921800

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