The size of a Minkowski ellipse that contains the unit ball |
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| Authors: | Marco Baronti Emanuele Casini Carlo Franchetti |
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| Institution: | 1. Dipartimento di Ingegneria della Produzione, Termoenergetica e Modelli Matematici, P.le Kennedy Pad. D, 16129, Genova, Italy;2. Dipartimento di Fisica e Matematica, Via Valleggio 11, 22100, Como, Italy;3. Dipartimento di Sistemi e Informatica, Via di S. Marta 3, Firenze, Italy |
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| Abstract: | In this paper we study the minimum radius of Minkowski ellipses (with antipodal foci on the unit sphere) necessary to contain the unit ball of a (normed or) Minkowski plane. We obtain a general upper bound depending on the modulus of convexity, and in the special case of a so-called symmetric Minkowski plane (a notion that we will recall in the paper) we prove a lower bound, and also we obtain that 3 is the exact upper bound. |
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