On gradient estimates of the heat semigroups on step-two Carnot groups
Analysis of PDEs
2026-05-19 v3
Abstract
In this work, we give a sufficient condition for a step-two Carnot group to satisfy the quasi Bakry-\'Emery curvature condition. As an application, we establish the gradient estimate for the heat semigroup on the free step-two Carnot group with three generators . Moreover, high order gradient estimates and the Riemannian counterparts are also deduced under an extra condition.
Keywords
Cite
@article{arxiv.2405.08605,
title = {On gradient estimates of the heat semigroups on step-two Carnot groups},
author = {Sheng-Chen Mao and Ye Zhang},
journal= {arXiv preprint arXiv:2405.08605},
year = {2026}
}