On some properties of quasiplanes (Q1411433)

The authors give a description of a quasiplane in terms of the isoperimetric constant and the fundamental frequency. A quasiplane is the pre-image of the hyperplane \(\{y=(y_1, y_2, \dots , y_n) \in \mathbb R^n: y_1=0\}\) under a quasiconformal mapping of \(\mathbb R^n\) onto \(\mathbb R^n\) if \(n>2\). In case of \(n=2\) this pre-image is called a quasiline. The characterization of a quasiline goes back to the known result due to \textit{L. V. Ahlfors} and \textit{A. Beurling} [See Acta Math. 96, 125-142 (1956; Zbl 0072.29602)].