Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg


Analysis-Seminar Augsburg-München


Dr. Panu Lahti
Universität Augsburg

spricht am
Donnerstag, 22. November 2018
15:00 Uhr
Raum 2004 (L1)
über das Thema:

»BV functions and Federer's characterization of sets of finite perimeter in metric spaces«

We consider the theory of functions of bounded variation (BV functions) in the general setting of a complete metric space equipped with a doubling measure and supporting a Poincaré inequality. Such a theory was first developed by Ambrosio (2002) and Miranda (2003). I will give an overview of the basic theory and then discuss a metric space proof of Federer's characterization of sets of finite perimeter, i.e. sets whose characteristic functions are BV functions. This characterization states that a set is of finite perimeter if and only if the n-1-dimensional (in metric spaces, codimension one) Hausdorff measure of the set's measure-theoretic boundary is finite. The proof relies on fine potential theory in the case p=1, much of which seems to be new even in Euclidean spaces.


Hierzu ergeht herzliche Einladung.
Prof. Dr. Lisa Beck

[Impressum]      [Datenschutz],     Di 13-Nov-2018 09:58:12 MEZ