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The gradient estimate of subelliptic harmonic maps with a potential

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Abstract

In this paper, we investigate subelliptic harmonic maps with a potential from noncompact complete sub-Riemannian manifolds corresponding to totally geodesic Riemannian foliations. Under some suitable conditions, we give the gradient estimates of these maps and establish a Liouville type result.

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Acknowledgements

The author is greatly indebted to Professor Yuxin Dong for his kind guidance and constant encouragement. The author also would like to express his thanks to Professor Yibin Ren and Professor Gui Mu for valuable discussions and helpful suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Han Luo

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  1. Han Luo
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Correspondence to Han Luo.

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Conflict of Interest The author declares no conflict of interest.

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This work was supported by the NSFC (11771087, 12171091).

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Luo, H. The gradient estimate of subelliptic harmonic maps with a potential. Acta Math Sci 44, 1189–1199 (2024). https://doi.org/10.1007/s10473-024-0401-y

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  • DOI: https://doi.org/10.1007/s10473-024-0401-y

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