The subelliptic heat kernel on SU(2): Representations, Asymptotics and Gradient bounds

TL;DR

This paper investigates the subelliptic heat kernel on the SU(2) Lie group, exploring its representations, asymptotic behavior, and gradient bounds within the context of subriemannian geometry.

Contribution

It provides a detailed analysis of the subelliptic heat kernel on SU(2), including new asymptotic estimates and gradient bounds in a positively curved subelliptic setting.

Findings

Derived explicit representations of the heat kernel.

Established asymptotic behaviors of the heat kernel.

Proved gradient bounds for the subelliptic heat semigroup.

Abstract

The Lie group SU(2) endowed with its canonical subriemannian structure appears as a three-dimensional model of a positively curved subelliptic space. The goal of this work is to study the subelliptic heat kernel on it and some related functional inequalities.