Namespaces
Variants
Actions

Finite Riemann surface

From Encyclopedia of Mathematics
Revision as of 17:05, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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).

References

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


Comments

The notion of a finite Riemann surface should not be mixed up with that of a Riemann surface of finite type: A Riemann surface is of finite type if it can be imbedded in a compact Riemann surface such that 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: http://encyclopediaofmath.org/index.php?title=Finite_Riemann_surface&oldid=33781
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article