Gradient estimate and Liouville theorems for p-harmonic maps

2019/12/28 by Dong, Yuxin, Lin, Hezi · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.12506

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.

Cited by

• Gradient estimates for (p,V)-harmonic functions on Riemannian manifolds

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