Gromov hyperbolicity and quasihyperbolic geodesics
  We characterize Gromov hyperbolicity of the quasihyperbolic metric space (\Omega,k) by geometric properties of the Ahlfors regular length metric measure space (\Omega,d,\mu). The characterizing properties are called the Gehring--Hayman condition and the ball--separation condition. 
Pekka Koskela, P\"aivi Lammi and Vesna Manojlovi\'c
math.MG math.CV