On some determinant and matrix inequalities with a geometrical flavour

Chen, Ting

doi:10.1090/tran/7158

On some determinant and matrix inequalities with a geometrical flavour
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Trans. Amer. Math. Soc. 370 (2018), 5179-5208 Request permission

Abstract:

In this paper we study some determinant inequalities and matrix inequalities which have a geometrical flavour. We first examine some inequalities which place work of Macbeath in a more general setting and also relate to recent work of Gressman. In particular, we establish optimisers for these determinant inequalities. We then use these inequalities to establish our Main Theorem, which gives a geometric inequality of matrix type which improves and extends some inequalities of Christ.

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