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Existence of p-energy minimizers in homotopy classes and lifts of Newtonian maps

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Abstract

We study the notion of p-quasihomotopy in Newtonian classes of mappings and link it to questions concerning lifts of Newtonian maps, under the assumption that the target space is nonpositively curved. Using this connection we prove that every p-quasihomotopy class of Newtonian maps contains a minimizer of the p-energy if the target has hyperbolic fundamental group.

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Author notes

  1. Elefterios Soultanis

    Present address: Current address: Department of Mathematics of the University of Fribourg, Chemin Du Musee 23, CH-1700, Fribourg, Switzerland

Authors and Affiliations

  1. University of Helsinki, P.O. Box 68, Gustaf Hällströmin katu 2b, FI-00014, Helsinki, Finland

    Elefterios Soultanis

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  1. Elefterios Soultanis
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Correspondence to Elefterios Soultanis.

Additional information

The author was supported by the Academy of Finland, project no. 1252293, and the Väisälä Foundation.

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Soultanis, E. Existence of p-energy minimizers in homotopy classes and lifts of Newtonian maps. JAMA 137, 469–505 (2019). https://doi.org/10.1007/s11854-019-0001-2

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  • DOI: https://doi.org/10.1007/s11854-019-0001-2

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