Ghandehari, Mostafa Steinhardt’s inequality in the Minkowski plane. (English) Zbl 0746.52003 Bull. Aust. Math. Soc. 45, No. 2, 261-266 (1992). The main result of this paper states that in a Minkowski plane with unit circle \(E\), the product of the positive circumference of a covex body \(K\) and that of its polar dual is at least the square of the Euclidean length of the polar dual of \(E\), with equality if and only if \(K\) is a Euclidean unit circle. Reviewer: T.Bisztriczky (Calgary) Cited in 2 Documents MSC: 52A10 Convex sets in \(2\) dimensions (including convex curves) 52A40 Inequalities and extremum problems involving convexity in convex geometry 51B20 Minkowski geometries in nonlinear incidence geometry Keywords:Minkowski plane; polar dual; circumference; Radon curves PDFBibTeX XMLCite \textit{M. Ghandehari}, Bull. Aust. Math. Soc. 45, No. 2, 261--266 (1992; Zbl 0746.52003) Full Text: DOI References: [1] DOI: 10.1007/BF01228179 · Zbl 0251.52003 [2] DOI: 10.1007/BF02759718 · Zbl 0168.19803 [3] DOI: 10.1112/blms/7.3.271 · Zbl 0311.52002 [4] DOI: 10.1007/BF01224933 · Zbl 0429.52001 [5] Eggleston, Convexity (1958) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.