Revista Matemática Iberoamericana

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Volume 33, Issue 3, 2017, pp. 951–994
DOI: 10.4171/RMI/960

Published online: 2017-10-02

Homotopy classes of Newtonian maps

Elefterios Soultanis[1]

(1) Polish Academy of Sciences, Warsaw, Poland

In this paper we study notions of homotopy in the Newtonian space $N^{1,p}(X;Y)$ of Sobolev type maps between metric spaces. After studying the properties and relations of two different notions we prove a compactness result for sequences in homotopy classes with controlled homotopies.

Keywords: Function spaces, metric measure spaces, Poincar´e inequality, homotopy

Soultanis Elefterios: Homotopy classes of Newtonian maps. Rev. Mat. Iberoam. 33 (2017), 951-994. doi: 10.4171/RMI/960