Gradient Estimate of subelliptic harmonic maps with potential

TL;DR

This paper studies subelliptic harmonic maps with potential on noncompact sub-Riemannian manifolds, providing gradient estimates and a Liouville type theorem under certain conditions.

Contribution

It introduces gradient estimates and Liouville theorems for subelliptic harmonic maps with potential, extending previous results to noncompact settings.

Findings

Gradient estimates for subelliptic harmonic maps with potential

Liouville type theorem established under certain conditions

Extension to noncompact complete sub-Riemannian manifolds

Abstract

In this paper, we investigate subelliptic harmonic maps with potential from noncompact complete sub-Riemannian manifolds corresponding to totally geodesic Riemannian foliations. Under some suitable conditions, we give the gradient estimates of these maps and establish a Liouville type result.