Complex rigidity of Teichm\"uller spaces
  We outline old and new results concerning the well-known problems in the Teichm\"uller space theory, i.e., whether these spaces are starlike in the Bers holomorphic embedding and whether any Teichm\"uller space of dimension greater than 1 is biholomorhically equivalent to bounded convex domain in a complex Banach space. 
Samuel L. Krushkal
math.CV