Classification of negatively pinched manifolds with amenable fundamental   groups
  We give a diffeomorphism classification of pinched negatively curved manifolds with amenable fundamental groups, namely, they are precisely the M\"obius band, and the products of a line with the total spaces of flat vector bundles over closed infranilmanifolds. 
Igor Belegradek (Georgia Tech), Vitali Kapovitch (University of   Maryland)