https://msp.org/pjm/2020/305-1/pjm-v305-n1-p11-s.pdf

Liouville-type theorems for weighted p-harmonic 1-forms and weighted p-harmonic maps

In this paper, we will show vanishing theorem of p harmonic 1 form on submanifold M in ¯ M whose BiRic curvature satisfying BiRic a ≥ Φ a ( H, S ). As an corollary, we can get the corresponding theorem for p harmonic function and p harmonic map. We also investigate the ﬁniteness problem of p harmonic 1 form on submanifold M in ¯ M whose BiRic curvature satisfying BiRic a ≥ − k 2 .

Vanishing theorem and finiteness theorem for $p$-harmonic $1$ form

In this paper, we will use the normalized intetral Ricci curvature to investigate Liouville type property of p harmonic function on Riemannian manifold. secondly, we will use the BiRic curvature to obtian Liuville theorem for p harmonic function or p harmonic 1 form. Lastly, we we will use the BiRic curvature to obtian Liouville theorem forhar-monic q ( q ≥ 2) form.

Liouville Type Theorem about $p$-harmonic 1 form, $p$-harmonic map and harmonic $ q $ form

Let M be a weighted Riemannian manifold with non-negative Bakry-Emery-Ricci curvature and N be a complete Riemannian manifold of non-positive sectional curvature. In this paper, the p-harmonic map u: M → N is studied, and a theorem of Liouville type is obtained.

/pdf/a-theorem-of-liouville-type-for-p-harmonic-maps-in-weighted-150xr1prul.pdf

Jian-Feng Zhang

Papers

A theorem of Liouville type for p-harmonic maps in weighted Riemannian manifolds