BZ Seminar in Analysis: Aldo Pratelli (Erlangen-Nürnberg)

New results on the isoperimetric problem with density

The isoperimetric problem in an Euclidean space where volume and perimeter are weighed by using a given density is studied since many decades. While a lot is classically known for specific cases (for instance the Gaussian case, or the case with density given by a power), in the case of a general distance there are a lot of open questions, for instance about existence and regularity of isoperimetric sets. We will discuss the general problem, giving some examples, and then we will discuss some recent results valid for general densities; in particular, we will see a sharp result about existence, and one about boundedness of isoperimetric sets.

Veranstaltung übernehmen als iCal