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Liouville theorems of subelliptic harmonic maps
Annals of Global Analysis and Geometry  (IF0.846),  Pub Date : 2021-11-22, DOI: 10.1007/s10455-021-09811-3
Gao, Liu, Lu, Lingen, Yang, Guilin

In this paper, we discuss two Liouville-type theorems for subelliptic harmonic maps from sub-Riemannian manifolds to Riemannian manifolds. One is the Dirichlet version which states that two subelliptic harmonic maps from a sub-Riemannian manifold with boundary to a regular ball must be same if their restrictions on boundary are same; it is generalized to complete noncompact domains as well. The other is the vanishing-type theorem for finite \(L^p\)-energy subelliptic harmonic maps on complete noncompact totally geodesic Riemannian foliations which are special sub-Riemannian manifolds.