A rigidity theorem with capacity and its applications

Lihe Wang, University of Iowa

Please note different day (Thursday) and time (4:30).   We will proof a rigidity theorem about subset in R^n that if a set is, in terms of capacity, like a cone at each of its boundary point in most of the scales, then it is either the whole space or half space. Its consequences to the regularity is also discussion from a local version of the theorem.