Rigid sets in the plane |
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| Authors: | Jon Aaronson Eli Glasner Michal Misiurewicz |
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| Institution: | (1) School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Israel;(2) Mathematical Institute, Warsaw University, Warsaw, Poland |
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| Abstract: | A compact set in the plane is rigid with respect to a norm if the norm isometries of the set act transitively on it. We show
that if a norm has an infinite rigid set, then, up to linear transformation, the norm is Euclidean and the set is a circle.
Our methods also yield a new characterisation of the ellipse. |
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