@inbook{10.4169/j.ctt6wpwc3.9,
ISBN = {9780883853382},
URL = {http://www.jstor.org/stable/10.4169/j.ctt6wpwc3.9},
abstract = {The main objects of study in this chapter are holomorphic functions$h:U \to V$, withUandVopen in C, that are one-to-one and onto. Such a holomorphic function is called aconformal(orbiholomorphic) mapping. The fact thathis supposed to be one-to-one implies that${h'}$is nowhere zero on U (remember that if${h'}$vanishes to order$k \geqslant 0$at a point$P\in U$, thenhis$(k + 0)$-to-1 in a small neighborhood ofP—see §§5.2.1). As a result,${h^{ - 1}}:V \to U$is also holomorphic, as we discussed in §§5.2.1. A conformal map$h:U \to V$from one open set to another can be},
bookauthor = {Steven G. Krantz},
booktitle = {A Guide to Complex Variables},
edition = {1},
pages = {83--94},
publisher = {Mathematical Association of America},
title = {The Geometric Theory of Holomorphic Functions},
volume = {32},
year = {2008}
}