The subject of conformal mappings is a major part of geometric
function theory that gained prominence after the publication of the
Riemann mapping theorem - for every simply connected domain of the
extended complex plane there is a univalent and meromorphic
function that maps such a domain conformally onto the unit disk.
The Handbook of Conformal Mappings and Applications is a compendium
of at least all known conformal maps to date, with diagrams and
description, and all possible applications in different scientific
disciplines, such as: fluid flows, heat transfer, acoustics,
electromagnetic fields as static fields in electricity and
magnetism, various mathematical models and methods, including
solutions of certain integral equations.
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