Namespaces
Variants
Actions

Multi-sheeted region

From Encyclopedia of Mathematics
Revision as of 17:08, 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 region of a Riemann surface , considered as a covering surface over the complex plane , such that above each point of its projection there are at least two points of ; a branch point of of order is regarded here as distinct points. For example, the analytic function is a one-to-one mapping of the disc onto the two-sheeted region (two-sheeted disc) of the Riemann surface of this function; this mapping is conformal everywhere except at the origin.

For analytic functions of several complex variables there arise multi-sheeted Riemann domains (cf. Riemannian domain) over the complex space .


Comments

References

[a1] C.L. Siegel, "Topics in complex functions" , 1 , Wiley (Interscience) (1988) pp. Chapt. 1, Sect. 4
[a2] G. Springer, "Introduction to Riemann surfaces" , Addison-Wesley (1957) pp. Chapt.10
How to Cite This Entry:
Multi-sheeted region. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Multi-sheeted_region&oldid=47922
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article