English

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 N3,2N_{3,2}. 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}
}