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