Dirichlet problem on Riemann Surfaces, V. On covering surfaces

The Dirichlet problem on quadratic surfaces

We give a fast, exact algorithm for solving Dirichlet problems with polynomial boundary functions on quadratic surfaces in Rn such as ellipsoids, elliptic cylinders, and paraboloids. To produce this algorithm, first we show that every polynomial in Rn can be uniquely written as the sum of a harmonic function and a polynomial multiple of a quadratic function, thus extending a theorem of Ernst Fi...

Computing on Riemann Surfaces

These notes are a review on computational methods that allow us to use computers as a tool in the research of Riemann surfaces, algebraic curves and Jacobian varieties. It is well known that compact Riemann surfaces, projective algebraiccurves and Jacobian varieties are only diierent views to the same object, i.e., these categories are equivalent. We want to be able to put our hands on this equ...

Coalescence on Riemann Surfaces

We consider coalescing fermions on a Riemann Surface and derive generalized determinant formulas, complementing some results of 3].

Uniform Approximation on Riemann Surfaces

This thesis consists of three contributions to the theory of complex approximation on Riemann surfaces. It is known that if E is a closed subset of an open Riemann surface R and f is a holomorphic function on a neighbourhood of E, then it is “usually” not possible to approximate f uniformly by functions holomorphic on all of R. In Chapter 2, we show, however, that for every open Riemann surface...

Complex Analysis on Riemann Surfaces