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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Aaronson, J., Glasner, E. & Misiurewicz, M. Rigid sets in the plane. Israel J. Math. 68, 307–326 (1989). https://doi.org/10.1007/BF02764987
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DOI: https://doi.org/10.1007/BF02764987