Some New Elements of the Elliptic Brunn-Minkowski Theory

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Published: Nov 12, 2018
Keywords:
Minkowski inequality, Brunn-Minkowski inequality, Kneser-Süss inequality, Minkowski’s determinant inequality, Blaschke summation, Matrix Blaschke summation, Mixed determinant, Matrix Kneser-Süss inequality

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Poramate Pranayanuntana
Department of Control Engineering, Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang (KMITL), Bangkok, Thailand

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: [email protected]

Article Details

Issue
Vol. 5 No. 1 (2005)
Section
Original Research Articles

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References

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