Algebraic topology Fundamental group and covering spaces Concept
Simply connected domain
Summary
A simply connected domain is a path-connected set in which each closed loop can be shrunk continuously to a point without leaving the set. Informally, the set is in one piece and has no hole that a loop can go around. On such domains, curl-free vector fields are conservative.
Where this leads
12 pages build on this one.
- Conformal invariance of harmonic functions
- Bendixson–Dulac theorem
- Green's function and the Riemann map
- Brennan conjecture
- Makarov's theorem on harmonic measure
- Local existence of harmonic conjugates
- Conformal radius
- Harmonic functions on Riemann surfaces
- Liouville's theorem for planar harmonic functions
- Bourgain's dimension bound for harmonic measure
- Parabolic and hyperbolic Riemann surfaces
- Weierstrass–Enneper parameterization
Further reading
- Web https://en.wikipedia.org/wiki/Simply_connected_space, lead section
About this page
| Tag | 0QW64ARSHB |
|---|---|
| URI | m2://0QW64ARSHB |
| Aliases | simply-connected-space |
| Kind | concept |
| Writing | W1 stated |
| MSC | 55Q05 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (1 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Used by
- Bendixson–Dulac theorem
- Green's function and the Riemann map
- Brennan conjecture
- Makarov's theorem on harmonic measure
- Local existence of harmonic conjugates
- Conformal radius
- Weierstrass–Enneper parameterization