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

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Abstract

We prove that a map f : M → N 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.

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Authors and Affiliations

  1. Dipartimento di Fisica e Matematica, Università dell’Insubria- Como, via Valleggio 11, 22100, Como, Italy

    Stefano Pigola

  2. Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133, Milano, Italy

    Giona Veronelli

Authors
  1. Stefano Pigola
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  2. Giona Veronelli
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Correspondence to Stefano Pigola.

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Pigola, S., Veronelli, G. On the homotopy class of maps with finite p-energy into non-positively curved manifolds. Geom Dedicata 143, 109–116 (2009). https://doi.org/10.1007/s10711-009-9376-z

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  • DOI: https://doi.org/10.1007/s10711-009-9376-z

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