This paper is part of a larger project initiated with [2]. Thefinal aim of the present paper is to give bounds for the homogenized (oreffective) conductivity in two dimensional linear conductivity. The main focus istherefore the periodic setting. We prove new variational principles thatare shown to be of interest in finding bounds on the homogenizedconductivity. Our results unify previous approaches by the second author and maketransparent the central role of quasiconformal mappings in all the two dimensionalG-closure problems in conductivity.
