Functions of a complex variable Basic notions Concept
Conformal map
Summary
A conformal map is a map that preserves angles and their orientation at each point, but not necessarily lengths, see the definition. In the plane, the conformal maps on an open set are the holomorphic functions with a derivative that is never zero.
Where this leads
14 pages build on this one.
- Conformal invariance of harmonic functions
- External ray
- Green's function and the Riemann map
- Brennan conjecture
- Conformal radius
- Plateau's problem
- Siegel disc
- Douglas–Radó solution of Plateau's problem
- Schwarz triangle function
- Liouville's theorem on conformal mappings
- Herman ring
- Harmonic functions on Riemann surfaces
- Conformal geometry
- Weierstrass–Enneper parameterization
Further reading
- Web https://en.wikipedia.org/wiki/Conformal_map, lead section
About this page
| Tag | 0YYT36R4YD |
|---|---|
| URI | m2://0YYT36R4YD |
| Aliases | conformal-mapping, angle-preserving-map |
| Kind | concept |
| Writing | W1 stated |
| MSC | 30C35 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Special cases
Definitions
Results about this
- Conformal invariance of harmonic functions
- Carathéodory's theorem on boundary extension
- Green's function and the Riemann map
- Brennan conjecture
- Liouville's theorem on conformal mappings
Used by
- Conformal invariance of harmonic functions
- External ray
- Green's function and the Riemann map
- Brennan conjecture
- Conformal radius
- Plateau's problem
- Siegel disc
- Douglas–Radó solution of Plateau's problem
- Schwarz triangle function
- Liouville's theorem on conformal mappings
- Herman ring
- Conformal geometry
- Weierstrass–Enneper parameterization