Equidimensional isometric maps

Bernd Kirchheim, Emanuele Spadaro, and László Székelyhidi

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Submission date: 28. Aug. 2014
Pages: 30
published in: Commentarii mathematici Helvetici, 90 (2015) 4, p. 761-798 
DOI number (of the published article): 10.4171/CMH/370
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Abstract:
In Gromov’s treatise (Partial differential relation, volume 9 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 1986), a continuous map between Riemannian manifolds is called isometric if it preserves the length of rectifiable curves. In this note we develop a method using the Baire category theorem for constructing such isometries. We show that a typical 1-Lipschitz map is isometric in canonically formulated extension and restriction problems.