Bounded variation functions form an important class in metric measure spaces. In this work we studied their infinitesimal regularity, which has recently played a role in resolving problems in theoretical computer science. Further developing tools to study this function class is useful both from a theoretical perspective but also may yield useful insights and tools for practical problems. The isoperimetry problems arise also in other contexts, such as in the joint work with Jasun Gong on Carpets in the plane satisfying a (1,1)-Poincaré inequality.
Asymptotic behavior of BV functions and sets of finite perimeter in metric measure spaces. Joint with James T. Gill, Panu Lahti, Nageswari Shanmugalingam. submitted, 2018