Characterizing the unit ball by its projective automorphism group

TL;DR

This paper explores the automorphism groups of domains in various projective spaces, providing new characterizations of the unit ball based on automorphism group size and boundary regularity.

Contribution

It introduces two novel characterizations of the unit ball using automorphism group size and boundary regularity in different projective spaces.

Findings

Characterizations of the unit ball via automorphism group size

Boundary regularity as a criterion for the unit ball

Applicable to real, complex, and quaternionic projective spaces

Abstract

In this paper we study the projective automorphism group of domains in real, complex, and quaternionic projective space and present two new characterizations of the unit ball in terms of the size of the automorphism group and the regularity of the boundary.