Conformal extensions of functions defined on arbitrary subsets of   Riemann surfaces
  For a function defined on an arbitrary subset of a Riemann surface, we give conditions which allow the function to be extended conformally. One folkloric consequence is that two common definitions of an analytic arc in ${\mathbb C}$ are equivalent.   Key-words: analytic continuation; analytic arc. 
P. M. Gauthier and V. Nestoridis
math.CV