Timeline for Existence of an inverse to the Schwarz-Christoffel mapping [closed]

Current License: CC BY-SA 4.0

12 events

when toggle format	what		by	license	comment
Apr 30, 2021 at 23:21	vote	accept	Talmsmen
Apr 30, 2021 at 20:23	history	closed	Alexandre Eremenko Kostya_I Mark Wildon alvarezpaiva Alec Rhea		Needs details or clarity
Apr 7, 2021 at 12:00	comment	added	Alexandre Eremenko		What do you mean by a "general formula" and formula for what? Schwarz-Christoffel map IS a formula. Are you asking whether the map or its inverse is an elementary function or what? Or conditions under which it is injective? Can you state your question precisely?
Apr 7, 2021 at 7:29	answer	added	Sam Nead		timeline score: 1
Apr 7, 2021 at 6:57	comment	added	Kostya_I		@JPwin, no, there's in general no explicit formula in terms of elementary functions. For example, for rectangles you can write a formula using elliptic functions, for triangles, the Schwarz-Cristoffel map gives you a hypergeometric function (and the inverse is rather obscure function)
Apr 7, 2021 at 5:59	history	edited	YCor	CC BY-SA 4.0	removed capitals
Apr 7, 2021 at 4:42	review	Close votes
Apr 30, 2021 at 20:23
Apr 7, 2021 at 4:26	history	edited	Daniele Tampieri	CC BY-SA 4.0	Typo fixing
Apr 7, 2021 at 1:00	comment	added	Talmsmen		Is there a general formula that could work for all polygonal geometries? Do you know of one?
Apr 7, 2021 at 0:45	comment	added	Alexandre Eremenko		Schwarz-Christoffel map is not always injective. When it is injective, the inverse map (from its image to the upper half-plane) of course exists. So what is your question exactly? This inverse map is sometimes an elementary function, as in your example. In most cases it is not.
Apr 7, 2021 at 0:33	history	edited	Talmsmen	CC BY-SA 4.0	added 244 characters in body
Apr 7, 2021 at 0:23	history	asked	Talmsmen	CC BY-SA 4.0