L\u3csup\u3e∞\u3c/sup\u3e-extremal Mappings in Amle and Teichmüller Theory

These lecture focus on two vector-valued extremal problems which have a common feature in that the corresponding energy functionals involve L ∞ norm of an energy density rather than the more familiar L p norms. Specifically, we will address (a) the problem of extremal quasiconformal mappings and (b) the problem of absolutely minimizing Lipschitz extensions