# Gromov's weak flexibiliy and counter-intuitive applications

**Date**: Monday 1 October 2018, 16:00 – 17:00**Location**: Mathematics Level 8, MALL 1 & 2, School of Mathematics**Type**: Pure Mathematics Colloquium, Seminars, Pure Mathematics, Colloquia**Cost**: Free

#### Christian Bär (Potsdam)

In his famous book on partial differential relations Gromov formulates a "weak flexibility lemma" as an exercise. We will discuss this lemma and sketch a proof. It can be applied in many different areas of mathematics. We will discuss a few applications:

1) How to make a roller coaster more exciting without violating safety regulations

2) Construction of a Lipschitz function with derivative >=1 "almost everywhere" which does not increase

3) Approximate a given surface in 3-space by C^{1,1}-surfaces with positive curvature "almost everywhere".

It is impossible to find a function as in 2) which is C nor can the approximation in 3) been done by C 1-surfaces. 2

The talk is based on joint work with Bernhard Hanke (Augsburg)