In this paper we study the minimum radius of Minkowski ellipse (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, in 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.
The size of a Minkowski ellipse that contains the unit ball
BARONTI, MARCO;
2012-01-01
Abstract
In this paper we study the minimum radius of Minkowski ellipse (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, in 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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