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Liouville-Type Theorems for CC-F-Harmonic Maps into a Carnot Group

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Abstract

In this paper, we introduce a horizontal F-energy functional for maps from a Riemannian manifold to a Carnot group. The critical maps of this functional are referred to as CC-F-harmonic maps. Under suitable conditions on the Hessian of the distance function and the degree of F(t), we obtain several Liouville-type theorems for CC-F-harmonic maps from some complete Riemannian manifolds to Carnot groups by assuming either growth condition of the horizontal F-energy or an asymptotic condition at the infinity for the maps.

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Authors and Affiliations

  1. School of Mathematic and Statistics, Anhui Normal University, Wuhu, 241000, P.R. China

    Guoqing He

  2. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, P.R. China

    Jing Li & Peibiao Zhao

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  1. Guoqing He
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  2. Jing Li
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  3. Peibiao Zhao
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Correspondence to Peibiao Zhao.

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This work is supported by NNSF of China (No. 11871275) and by Research Found for the Doctoral Program of Anhui Normal University (CN) (No. 751841)

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He, G., Li, J. & Zhao, P. Liouville-Type Theorems for CC-F-Harmonic Maps into a Carnot Group. J Geom Anal 31, 4024–4050 (2021). https://doi.org/10.1007/s12220-020-00424-z

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  • DOI: https://doi.org/10.1007/s12220-020-00424-z

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