Equidimensional isometric maps
Bernd Kirchheim
Universität Leipzig, GermanyEmanuele Spadaro
Max-Planck-Institut Mathematik in den Naturwissenschaften, Leipzig, GermanyLászló Székelyhidi Jr.
Universität Leipzig, Germany
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Abstract
In Gromov’s treatise (Partial differential relations, 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.
Cite this article
Bernd Kirchheim, Emanuele Spadaro, László Székelyhidi Jr., Equidimensional isometric maps. Comment. Math. Helv. 90 (2015), no. 4, pp. 761–798
DOI 10.4171/CMH/370