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...ut not necessarily the size of geometric figures) are also [[conformal map|conformal]] (locally preserve shape). Similarity transformations which fix the origin ...tions. However, [[shear transformation]]s and non-uniform scaling are not. Conformal linear transformations come in two types, ''proper'' transformations preser ...

...efore Möbius transformation.svg|frame|A coordinate grid prior to a special conformal transformation]] ...l grid after Möbius transformation.svg|frame|The same grid after a special conformal transformation]] ...

...f the distortion of a function is equal to one, then it is [[conformal map|conformal]]; if the distortion is bounded and the function is a [[homeomorphism]], th ...last1=Reshetnyak | first1=Yu. G.|authorlink=Yurii Reshetnyak | title=Space mappings with bounded distortion | publisher=[[American Mathematical Society]] | loc ...

...f [[Holomorphic function|holomorphic]] [[univalent function|univalent self-mappings]] of the [[unit disk]], called a '''Loewner semigroup'''. This semigroup co ...late 1990s, has been extensively developed in [[probability theory]] and [[conformal field theory]]. ...

{{short description|Conformal mappings in complex analysis}} ...warz triangle function''' or '''Schwarz s-function''' is a function that [[conformal mapping|conformally maps]] the [[upper half plane]] to a triangle in the up ...

...alytic functions of several variables are not [[conformal map|conformal]]. Conformal maps can be defined between Euclidean spaces of arbitrary dimension, but wh ...Zorich]]<ref name="resh2">{{cite book|author=Yu. G. Reshetnyak|title=Space mappings with bounded distortion| ...

...|an open set covering of the [[sierpinski triangle]] along with one of its mappings ψ_''i''.]] ...iven an [[iterated function system]] of [[contraction mapping| contractive mappings]] <math>\psi_1, \ldots, \psi_m</math>, the open set condition requires that ...

| known_for = [[Quasi-conformal mappings]] ...atician who worked in the area of [[complex analysis]] ([[quasi-conformal mappings]]). ...

...}}</ref> {{harvtxt|Sharon|Mumford|2006}} describe the first two methods of conformal welding as well as providing numerical computations and applications to the '''conformal welding''' condition: ...

| contribution = Planar conformal mappings of piecewise flat surfaces ...e-distance circle packings have been used to construct approximations to [[conformal mapping]]s.<ref name="bh"/> ...

...symmetric map|quasisymmetric homeomorphism]] of the circle, then there are conformal maps ''f'' of [''z''| < 1 and ''g'' of |''z''|>1 into disjoint regions suc Conversely, using the [[Riemann mapping theorem]], the conformal maps ''f'' and ''g'' uniformizing the outside of a quasicircle give rise to ...

...plex, multi-complex, and split-quaternionic variables and their associated conformal geometries], Ph.D. Thesis, [[Florida State University]] [[Category:Functions and mappings]] ...

...[univalent function|univalent holomorphic mapping]], or a [[semigroup]] of mappings, of the [[unit disk]] in the [[complex numbers]] into itself. ...ntified with the open domain {{math|''U'' {{=}} ''h''(''D'')}}. Under this conformal identification, the mapping &nbsp; {{mvar|f}} becomes multiplication by { ...

| title=Conformal welding and Koebe's theorem | title=Conformal mapping in linear time ...

* [[Conformal transformation]]s preserve angles, and are, in the first order, similaritie Fconf.gif | [[Conformal transformation]] ...

...ralization of the [[uniformization theorem]], that every such surface is [[conformal equivalence|conformally equivalent]] to either the Riemann sphere or the co ...''C''' ∪ ∞, in which case the Riemann surface is compact and ''f'' gives a conformal equivalence with the Riemann sphere; or the complement of the image is a un ...

'''Conformal geometric algebra''' ('''CGA''') is the [[geometric algebra]] constructed o <!--This paragraph extends the conformal idea to generalized "conformal geometric objects"--> ...

Mappings of the form <math>z \mapsto \frac{pz - q}{\bar q z + \bar p}</math> express == Conformal interpretation == ...

...eometry of polynomials, [[special functions]], [[Hardy spaces]], conformal mappings (including numerical analysis). and potential theory (minima of energy unde ...

...orem]] and the [[simultaneous uniformization theorem]]. The existence of [[conformal welding]]s can also be derived using the Beltrami equation. One of the simp The solution ''f'' is a quasiconformal conformal diffeomorphism. These form a group and their Beltrami coefficients can be c ...