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

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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Correspondence to Elefterios Soultanis.

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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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