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Gradient Estimate and Liouville Theorems for p-Harmonic Maps

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Abstract

In this paper, we first obtain an \(L^q\) gradient estimate for p-harmonic maps, by assuming the target manifold supporting a certain function, whose gradient and Hessian satisfy some analysis conditions. From this \(L^q\) gradient estimate, we get a corresponding Liouville type result for p-harmonic maps. Secondly, using these general results, we give various geometric applications to p-harmonic maps from complete manifolds with nonnegative Ricci curvature to manifolds with various upper bound on sectional curvature, under appropriate controlled images.

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Acknowledgements

The authors would also like to thank Professor G.F. Wang for his interest and suggestions. Yuxin Dong is supported by NSFC Grant No. 11771087. Hezi Lin is supported by NSFC Grant No. 11831005.

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Authors and Affiliations

  1. School of Mathematical Sciences and Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai, 200433, China

    Yuxin Dong

  2. College of Mathematics and Informatics & FJKLMAA, Fujian Normal University, Fuzhou, 350108, China

    Hezi Lin

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  1. Yuxin Dong
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  2. Hezi Lin
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Correspondence to Hezi Lin.

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Dong, Y., Lin, H. Gradient Estimate and Liouville Theorems for p-Harmonic Maps. J Geom Anal 31, 8318–8333 (2021). https://doi.org/10.1007/s12220-020-00594-w

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