Riemann mapping theorem
Let be a simply connected open proper subset of , and let . There is a unique analytic function such that
-
1.
, and is real and positive;
-
2.
is injective;
-
3.
.
Remark. As a consequence of this theorem, any two simply connected regions, none of which is the whole plane, are conformally equivalent.
Title | Riemann mapping theorem |
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Canonical name | RiemannMappingTheorem |
Date of creation | 2013-03-22 13:15:03 |
Last modified on | 2013-03-22 13:15:03 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 5 |
Author | Koro (127) |
Entry type | Theorem |
Classification | msc 30A99 |
Related topic | ConformalRadius |