Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. M. Gauthier, Complex extension-interpolation and approximation on arbitrary sets in one dimension (submitted).
P. M. Gauthier and V. Nestoridis, Conformal extensions of functions defined on arbitrary subsets of Riemann surfaces, arXiv:1406.3530
M. J. Greenberg, Lectures on algebraic topology, W. A. Benjamin, Inc., New York-Amsterdam 1967.
Nestoridis V., Zadik I.: Padé Approximants, density of rational functions in \({A^{\infty}(\Omega)}\) and smoothness of the integration operator, J. Math. Anal. Appl. 423, 1514–1539 (2015)
J. Milnor, Differential Topology, Lectures by John Milnor, Princeton University, Fall term 1958. Notes by James Munkres.
Osserman R.: A lemma on analytic curves, Pacific J. Math. 9, 165–167 (1959)
A. Pfluger, Theorie der Riemannschen Flächen, Springer, Berlin-Göttingen-Heidelberg, 1957.
Author information
Authors and Affiliations
Corresponding author
Additional information
Research supported by NSERC (Canada).
Rights and permissions
About this article
Cite this article
Gauthier, P.M., Nestoridis, V. Conformal extensions of functions defined on arbitrary subsets of Riemann surfaces. Arch. Math. 104, 61–67 (2015). https://doi.org/10.1007/s00013-014-0716-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-014-0716-3