The Weil-Petersson geometry of the five-times punctured sphere
  We give a new proof that the completion of the Weil-Petersson metric on Teichm\"uller space is Gromov-hyperbolic if the surface is a five-times punctured sphere or a twice-punctured torus. Our methods make use of the synthetic geometry of the Weil-Petersson metric. 
Javier Aramayona