### 22.11.2018 15:00 Panu Lahti (Universität Augsburg):BV functions and Federer's characterization of sets of finite perimeter in metric spacesRoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

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.