Geometriae Dedicata

, 143:109 | Cite as

On the homotopy class of maps with finite p-energy into non-positively curved manifolds

  • Stefano Pigola
  • Giona Veronelli
Original Paper


We prove that a map f : MN with finite p-energy, p > 2, from a complete manifold \({\left(M,\left\langle ,\right\rangle \right)}\) 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.


p-harmonic maps Liouville type theorem Homotopy class 

Mathematics Subject Classification (2000)

53C43 58E20 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Dipartimento di Fisica e MatematicaUniversità dell’Insubria- ComoComoItaly
  2. 2.Dipartimento di MatematicaUniversità di MilanoMilanoItaly

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