Journal of Geometry

, Volume 96, Issue 1, pp 1–10

Two non existence results for the self-similar equation in Euclidean 3-space

Article

DOI: 10.1007/s00022-010-0031-5

Cite this article as:
Anciaux, H. J. Geom. (2009) 96: 1. doi:10.1007/s00022-010-0031-5
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Abstract

We prove that the only self-similar surfaces of Euclidean 3-space which are foliated by circles are the self-similar surfaces of revolution discovered by S. Angenent and that the only ruled, self-similar surfaces are the cylinders over planar self-similar curves.

Mathematics Subject Classification (2000)

43C44

Keywords

Mean curvature flowself-similar solutioncyclic surfacesruled surfaces

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.IME, Bloco AUniversidade de São PauloSão PauloBrazil