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shupp_01

Prof. Dr. Bernd Kawohl, Universität zu Köln, Vortrag: Geometric Inequalities

Donnerstag, 09.06.2016 16:30 im Raum M5
Mathematik und Informatik

> Some geometric inequalities such as the classical isoperimetric > inequality are considerably easier to prove in two than in higher dimensions. > 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.



Angelegt am Dienstag, 05.04.2016 11:17 von shupp_01
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