We prove that a map f : M → N with finite p-energy, p > 2, from a complete manifold ( M , ⟨, ⟩) into a non-positively curved, compact manifold N is homotopic to a constant, provided the negative part of the Ricci curvature of the domain manifold is small in a suitable spectral sense. The result relies on a Liouville-type theorem for finite q-energy, p-harmonic maps under spectral assumptions.
On the homotopy class of maps with finite p-energy into non-positively curved manifolds
PIGOLA, STEFANO;
2009-01-01
Abstract
We prove that a map f : M → N with finite p-energy, p > 2, from a complete manifold ( M , ⟨, ⟩) into a non-positively curved, compact manifold N is homotopic to a constant, provided the negative part of the Ricci curvature of the domain manifold is small in a suitable spectral sense. The result relies on a Liouville-type theorem for finite q-energy, p-harmonic maps under spectral assumptions.
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