Isoperimetric problem in H-type groups and Grushin spaces

TL;DR

This paper investigates the isoperimetric problem within H-type groups and Grushin spaces, establishing existence, symmetry, and regularity of optimal sets and exploring their interrelation.

Contribution

It introduces new results on the existence and properties of isoperimetric sets in these geometric spaces, highlighting a connection between H-type groups and Grushin spaces.

Findings

Existence of isoperimetric sets proven

Symmetry and regularity properties established

Relation between H-type groups and Grushin spaces analyzed

Abstract

We study the isoperimetric problem in H-type groups and Grushin spaces, emphasizing a relation between them. We prove existence, symmetry and regularity properties of isoperimetric sets, under a symmetry assumption that depends on the dimension.