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arXiv · 1408.6737

Equidimensional isometric maps

Bernd Kirchheim·Emanuele Spadaro·Laszlo Szekelyhidi Jr
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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.

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Bernd Kirchheim, Emanuele Spadaro, Laszlo Szekelyhidi Jr. 2014-08-28. Equidimensional isometric maps. https://arxiv.org/abs/1408.6737

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