Liouville type theorem about p-harmonic function and p-harmonic map with finite L q -energy

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

“…A map u is called p-harmonic map if τ p (u) = div(|du| p−2 du) = 0. Motivated by [23], in [4], we studied the Liouville theorem of p harmonic map with finite energy from complete noncompact submanifold in partially nonnegative curved manifold into nonpositive curved manifold, the conditons in our theorem is the index of the operator ∆ + 1 4 (S − nH 2 ) is zero or the small conditon on S − nH 2 n 2 . In [16], Han obtained liouville type theorem for p harmonic function on submanifold in sphere.…”