Open Problems

Abstract

In the previous chapters we have discussed a subclass of Korotkin‚s hyperelliptic solutions to the Ernst equation with physically interesting properties. Physical and mathematical properties of the solutions havebeen studied analytically and numerically for in principle arbitrary genus of the solution. As an example we have presented the counter–rotating dust disk [130] which is given on a surface of genus 2, andwhich was obtained as the solution to a boundary value problem. What remains unclear is how to solve general boundary value problems with these Riemann surface techniques.