Gradient estimate and Liouville theorems for p-harmonic maps

Yuxin Dong; Hezi Lin

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arXiv · 1912.12506

Gradient estimate and Liouville theorems for p-harmonic maps

Yuxin Dong·Hezi Lin

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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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Yuxin Dong, Hezi Lin. 2019-12-28. Gradient estimate and Liouville theorems for p-harmonic maps. https://arxiv.org/abs/1912.12506

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