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.
Equidimensional isometric maps / Kirchheim, Bernd; Spadaro, EMANUELE NUNZIO; Székelyhidi, Laszlo. - In: COMMENTARII MATHEMATICI HELVETICI. - ISSN 0010-2571. - 90:4(2015), pp. 761-798. [10.4171/CMH/370]
Equidimensional isometric maps
Emanuele Spadaro;
2015
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.| File | Dimensione | Formato | |
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