On the Existence of Global Tchebychev Nets

Sandra L. Samelson, W. P. Dayawansa
1995 Transactions of the American Mathematical Society  
Let S be a complete, open simply connected surface. Suppose that the integral of the Gauss curvature over arbitrary measurable sets is less than tt/2 in magnitude. We show that the surface admits a global Tchebychev net.
doi:10.2307/2154907 fatcat:7tby34dxjjclfl6dpuogsazxbi