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.
Pigola, S., Veronelli, G. (2009). On the homotopy class of maps with finite p-energy into non-positively curved manifolds. GEOMETRIAE DEDICATA, 143(1), 109-116 [10.1007/s10711-009-9376-z].
On the homotopy class of maps with finite p-energy into non-positively curved manifolds
Pigola, Stefano;VERONELLI, GIONA
2009
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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