MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Equidimensional isometric maps

Bernd Kirchheim, Emanuele Spadaro and László Székelyhidi


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.


Related publications

2015 Repository Open Access
Bernd Kirchheim, Emanuele Spadaro and László Székelyhidi

Equidimensional isometric maps

In: Commentarii mathematici Helvetici, 90 (2015) 4, pp. 761-798