Speaker
Description
We will revisit the regularity properties of (quasi)minimizers and consider two types of minimizers involving the perimeter. One minimization is for the perimeter among sets with fixed volume, leading to isoperimetric sets and the other is a minimization of the perimeter with an additive term penalizing the deviation in measure from a given set.
In essentially non-branching MCP(K,N)-spaces, isoperimetric sets have nice topological properties and they are also perimeter quasiminimizers. However, in general PI-spaces isoperimetric sets need not be quasiminimizers and even their topological and measure theoretic boundaries can be drastically different.
With the other minimization having a penalization term we obtain BV-extension sets in metric measure spaces without any PI-assumption. For the extension properties the boundary plays a more subtle role.
The study of isoperimetric sets has been done with Enrico Pasqualetto and the minimiaztion giving BV-extension sets is from a joint work with Jesse Koivu and Danka Lučić.