Some New Elements of the Elliptic Brunn-Minkowski Theory
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Abstract
In this paper, we present various matrix analog of notions and inequalities in convex geometry. We employ the well known notion of mixed determinant - and analog of the notion of mixed volume in convex geometry, and introduce the matrix version of Blaschke summation – an analog of the notion of Blaschke summation for convex bodies. With these notions we then can develop some matrix analogs of the convex geometry. In this paper, we also present one new inequality analog – the matrix version of Kneser-Süss inequality.
Keywords: Minkowski inequality, Brunn-Minkowski inequality, Kneser-Süss inequality, Minkowski’s determinant inequality, Blaschke summation, Matrix Blaschke summation, Mixed determinant, Matrix Kneser-Süss inequality
Corresponding author: E-mail: ppranaya@duke.poly.edu
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References
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