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, Colloquium
- 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)