On the Cheng-Yau gradient estimate for Carnot groups and sub-Riemannian manifolds

TL;DR

This paper demonstrates how existing results can be used to establish the Cheng-Yau gradient estimate on Carnot groups and certain sub-Riemannian manifolds, extending classical geometric analysis tools to these settings.

Contribution

It applies known techniques to derive the Cheng-Yau estimate specifically for Carnot groups and sub-Riemannian manifolds with generalized curvature-dimension inequalities.

Findings

Cheng-Yau gradient estimate established for Carnot groups

Extension of the estimate to sub-Riemannian manifolds with curvature-dimension bounds

Demonstrates the applicability of previous results to new geometric contexts

Abstract

In this note we show how results in \cite{BaudoinBonnefont2016, BaudoinGarofalo2013, CoulhonJiangKoskelaSikora2017} yield the Cheng-Yau estimate on two classes of sub-Riemannian manifolds: Carnot groups and sub-Riemannian manifolds satisfying a generalized curvature-dimension inequality.