Title: Computable Riemann Surfaces

Abstract: In this paper we introduce computable and time bounded
Riemann surfaces, based on the classical abstract definition by charts.
Building upon this definition we discuss computable versions of several
classical results, such as the existence of complete continuations of
holomorphic functions, universal coverings and the uniformization theorem
(for some cases).
Though we state most of our results for computable surfaces, many of
them can also transformed into a uniform version, i.e. based on
representations of the class of Riemann surfaces (modulo conformal
equivalence).