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.

中文翻译：

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亚椭圆调和映射的刘维尔定理

在本文中，我们讨论了从亚黎曼流形到黎曼流形的亚椭圆调和映射的两个 Liouville 型定理。一个是狄利克雷版本，它指出如果边界限制相同，则从具有边界的亚黎曼流形到规则球的两个亚椭圆调和映射必须相同；它也被推广到完整的非紧凑域。另一个是有限\(L^p\) -能量亚椭圆调和映射在完全非紧致的全测地黎曼叶理上的消失型定理，这是特殊的亚黎曼流形。