Given a hyperelliptic hyperbolic surface S of genus g >= 2, we find bounds on the lengths of homologically independent loops on S. As a consequence, we show that for any lambda is an element of (0, 1) there exists a constant N(lambda) such that every such ...
We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface S where a short closed geodesic is pinched. If the geodesic separates the surface into two parts, then the Jacobian variety of S develops into a variety that split ...
In this paper, we continue to investigate the systolic landscape of translation surfaces started in [T. Columbus, F. Herrlich, B. Muetzel and G. Weitze-Schmithüsen, Systolic geometry of translation surfaces, Exp. Math. (2022), doi:10.1080/10586458.2022.210 ...
We present four counterexamples in surface homology. The first example shows that even if the loops inducing a homology basis intersect each other at most once, they still may separate the surface into two parts. The other three examples show some difficul ...
The authors define a family of functions by starting with (complex) exponentials and closing under some basic algebraic operations, integration, and solution of certain systems of differential equations. They then show that for every recursively (computabl ...
We investigate systems of ordinary differential equations with a parameter. We show that under suitable assumptions on the systems the solutions are computable in the sense of recursive analysis. As an application we give a complete characterization of the ...
The authors propose a numerical method for the uniformization of Riemann surfaces and algebraic curves in genus two with highly accurate results. Let G be a Fuchsian group acting on the unit disk BbbD, and let S=BbbD/G. It is well known that $S ...
