Riesz and Green energy on projective spaces

TL;DR

This paper investigates Riesz, Green, and logarithmic energies on various projective spaces, providing bounds using determinantal point processes to understand their energetic properties.

Contribution

It offers new upper and lower bounds for energies on projective spaces, extending the analysis to real, complex, quaternionic, and Cayley cases.

Findings

Established upper estimates for energies using determinantal point processes.

Derived lower bounds of the same order of magnitude for these energies.

Applied results to real, complex, quaternionic, and Cayley projective spaces.

Abstract

In this paper we study Riesz, Green and logarithmic energy on two-point homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projective spaces. For each of these spaces we provide upper estimates for the mentioned energies using determinantal point processes. Moreover, we determine lower bounds for these energies of the same order of magnitude.