paper

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

arXiv:0904.4269

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.

11 pages