Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Christian Bär
Affiliation:

Universität Potsdam
Date:

Thu, 2019-04-18 13:45 - 14:45 The Nash-Kuiper embedding theorem is a prototypical example of a counterintuitive approximation result: any short embedding of a Riemannian manifold into Euclidean space can be approximated by ***isometric*** ones. As a consequence, any surface can be isometrically C 1-embedded into an arbitrarily small ball in R 3. For C 2-embeddings this is impossible due to curvature restrictions.

We will present a general result which will allow for approximations by functions satisfying strongly overdetermined equations on open dense subsets. This will be illustrated by three examples: real functions,

embeddings of surfaces, and abstract Riemannian metrics on manifolds.

Our method is based on "weak flexibility", a concept introduced by Gromov in 1986. This is joint work with Bernhard Hanke.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/158

[4] http://www.mpim-bonn.mpg.de/node/4652

[5] http://www.mpim-bonn.mpg.de/node/9281