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Liouville theorems of subelliptic harmonic maps

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Abstract

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.

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (Grant No. 11771087).

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Author notes

  1. Lingen Lu and Guilin Yang these authors contributed equally to this work.

Authors and Affiliations

  1. Normal School, Jinhua Polytechnic, Jinhua, 321017, Zhejiang, People’s Republic of China

    Liu Gao

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Lingen Lu

  3. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, 201620, People’s Republic of China

    Guilin Yang

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  1. Liu Gao
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  2. Lingen Lu
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  3. Guilin Yang
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Correspondence to Liu Gao.

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Gao, L., Lu, L. & Yang, G. Liouville theorems of subelliptic harmonic maps. Ann Glob Anal Geom 61, 293–307 (2022). https://doi.org/10.1007/s10455-021-09811-3

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  • DOI: https://doi.org/10.1007/s10455-021-09811-3

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