Abstract:

This paper derives the sub-Laplacian estimates of the Riemannian distance function on foliated Riemannian manifolds, and applies this result to establish the gradient estimates and Liouville-type theorems for foliated subelliptic harmonic maps from complete non-compact foliated Riemannian manifolds to Cartan-Hadamard manifolds. }

Key words: Riemannian foliations, subelliptic harmonic maps, gradient estimates, Liouville theorems.