Heat kernel asymptotics on the free step-two Carnot group with $3$ generators
Analysis of PDEs
2023-12-27 v1 Probability
Abstract
In this work, we establish the uniform heat kernel asymptotics as well as sharp bounds for its derivatives on the free step-two Carnot group with generators. As a by-product, on this highly non-trivial toy model, we completely solve the Gaveau-Brockett problem, in other words, we obtain the expression of the squared Carnot-Carath\'eodory distance, as explicitly as one can possibly hope for. Furthermore, the precise estimates of the heat kernel, and its small-time asymptotic behaviors are deduced.
Cite
@article{arxiv.2312.15168,
title = {Heat kernel asymptotics on the free step-two Carnot group with $3$ generators},
author = {Hong-Quan Li and Sheng-Chen Mao and Ye Zhang},
journal= {arXiv preprint arXiv:2312.15168},
year = {2023}
}