Work

Complex and quaternionic analogues of Busemann’s random simplex and intersection inequalities

Year: 2025

Type: article

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.

Source: Mathematische Annalen

DOI: 10.1007/s00208-025-03279-3

Authors: Christos Saroglou, Thomas Wannerer

Institutions: University of Ioannina, Friedrich Schiller University Jena

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Deutsche Forschungsgemeinschaft