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arXiv · 2409.01057

Complex and Quaternionic Analogues of Busemann's Random Simplex and Intersection Inequalities

Christos Saroglou·Thomas Wannerer
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Abstract

In this paper, we extend two celebrated inequalities by Busemann -- the random simplex inequality and the intersection inequality -- to both complex and quaternionic vector spaces. Our proof leverages a monotonicity property under symmetrization with respect to complex or quaternionic hyperplanes. Notably, we demonstrate that the standard Steiner symmetrization, contrary to assertions in a paper by Grinberg, does not exhibit this monotonicity property.

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Christos Saroglou, Thomas Wannerer. 2024-09-02. Complex and Quaternionic Analogues of Busemann's Random Simplex and Intersection Inequalities. https://arxiv.org/abs/2409.01057

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