 In 2001, Sergei Ivanov presented another way to prove that the hemisphere has smallest area among isometric fillings homeomorphic to a disk.His argument does not employ the uniformization theorem and is based instead on the topological fact that two curves on a disk must cross if their four endpoints are on the boundary and interlaced.Moreover, Ivanov's proof applies more generally to disks with Finsler metrics, which differ from Riemannian metrics in that they need not satisfy the Pythagorean equation at the infinitesimal level.