Prof. Dr. Bernd Kawohl, Universität zu Köln, Vortrag: Geometric Inequalities
Donnerstag, 09.06.2016 16:30 im Raum M5
> Some geometric inequalities such as the classical isoperimetric
> inequality are considerably easier to prove in two than in higher
> In my lecture I will present two long conjectured and recently
> confirmed inequalities, for which already the proof in two dimensions
> presents a considerable challenge.
> The first one involves the elastic energy $\int_\gamma \kappa^2\,ds$
> of a plane closed curve $\gamma$ bounding a simply connected set $\Omega$.
> Given the area of $\Omega$, only the circle minimizes the elastic
> energy of $\Omega$.
> The second one relates the length of an area-bisecting shortest curve
> to the shape of the admissible convex plane set $\Omega$ of given area.
> Only the disc maximizes the length of this curve among all plane
> convex sets of given area.