Riemann surfaces with longest systole and an improved Voronoï algorithm (Q5937391)

The author introduces a new method in order to find the Riemannian surface \(M\) of a fixed topological type with the longest systole. This is based on a cell decomposition of the Teichmüller space of \(M\). The method also works in the Euclidean case and is similar to the so-called Voronoï algorithm for positive definite quadratic forms, or equivalently, for lattice sphere packings. The author gives a new proof of Rodgers' theorem.