The growth of the first non-Euclidean filling function of the quaternionic Heisenberg Group

TL;DR

This paper investigates the growth rates of filling volume functions in quaternionic Heisenberg groups, revealing that in certain dimensions, their growth surpasses that of Euclidean spaces, indicating unique geometric properties.

Contribution

It identifies the precise growth rate of the (n+1)-dimensional filling volume function in quaternionic Heisenberg groups, showing it exceeds Euclidean growth, which was previously unknown.

Findings

Growth rate of filling volume function in dimension n matches Euclidean space.

In dimension n+1, the growth rate is strictly faster than Euclidean.

Quaternionic Heisenberg groups exhibit unique geometric filling properties.

Abstract

The filling volume functions of the n-th quaternionic Heisenberg group grow, up to dimension n, as fast as the ones of the Euclidean space. We identify the growth rate of the filling volume function in dimension n+1, which is strictly faster than the growth rate of the (n+1)-dimensional filling volume function of the Euclidean space.