Convexity of length functions and Thurston's shear coordinates
  We show that the length function of a measured geodesic lamination is convex in Thurston's shear coordinates over Teichm\"uller space and strictly convex for generic laminations. We give some consequences of this result in the context of Thurston's asymmetric metric on Teichm\"uller space. 
Guillaume Th\'eret
math.GT