Difference between revisions of "Finite Riemann surface"
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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|Riemann surfaces, classification of]] and (the references to) [[Double of a Riemann surface|Double of a Riemann surface]]. | 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|Riemann surfaces, classification of]] and (the references to) [[Double of a Riemann surface|Double of a Riemann surface]]. | ||
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Latest revision as of 10:51, 18 October 2014
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 $M$ 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: http://encyclopediaofmath.org/index.php?title=Finite_Riemann_surface&oldid=33782
Finite Riemann surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Finite_Riemann_surface&oldid=33782
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article