Finite Riemann surface

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A Riemann surface of finite genus (cf. Genus of a surface) having finitely many non-degenerate boundary components. A finite Riemann surface can be imbedded in a closed Riemann surface — its double (cf. Double of a Riemann surface).


[1] M. Schiffer, D.C. Spencer, "Functionals of finite Riemann surfaces" , Princeton Univ. Press (1954)


The notion of a finite Riemann surface should not be mixed up with that of a Riemann surface of finite type: A Riemann surface $M$ is of finite type if it can be imbedded in a compact Riemann surface $\tilde M$ such that $\tilde M \setminus M$ consists of finitely many points. Cf. also Riemann surfaces, classification of and (the references to) Double of a Riemann surface.

How to Cite This Entry:
Finite Riemann surface. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article