 The area of a Finsler surface can be defined in various inequivalent ways, and the one employed here is the Holmes–Thompson area, which coincides with the usual area when the metric is Riemannian.What Ivanov proved is that

Let be a Finsler disk that isometrically fills its boundary of length .We may assume that is the standard round disk in , and the Finsler metric is smooth and strongly convex.