On some determinant and matrix inequalities with a geometrical flavour
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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.References
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Additional Information
- Ting Chen
- Affiliation: School of Mathematics, University of Edinburgh, Edinburgh, EH9 3JZ, United Kingdom
- MR Author ID: 1174334
- Email: zirui20082008@163.com
- 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.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 5179-5208
- MSC (2010): Primary 26B25, 26D20, 42B99
- DOI: https://doi.org/10.1090/tran/7158
- MathSciNet review: 3787381