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Transactions of the American Mathematical Society

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On some determinant and matrix inequalities with a geometrical flavour

Author: Ting Chen
Journal: Trans. Amer. Math. Soc. 370 (2018), 5179-5208
MSC (2010): Primary 26B25, 26D20, 42B99
Published electronically: March 21, 2018
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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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Additional Information

Ting Chen
Affiliation: School of Mathematics, University of Edinburgh, Edinburgh, EH9 3JZ, United Kingdom

Keywords: Matrix inequalities, determinant inequalities, symmetrisation, rearrangements, optimisers, sharp constants.
Received by editor(s): June 13, 2016
Received by editor(s) in revised form: November 30, 2016
Published electronically: March 21, 2018
Additional Notes: This work was supported by a scholarship from the China Scholarship Council.
Article copyright: © Copyright 2018 American Mathematical Society

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