Rahul Sharma (Editor)

Radó's theorem (harmonic functions)

Updated on
Share on FacebookTweet on TwitterShare on LinkedInShare on Reddit
Covid-19

In mathematics, Radó's theorem is a result about harmonic functions, named after Tibor Radó. Informally, it says that any "nice looking" shape without holes can be smoothly deformed into a disk.

Suppose Ω is an open, connected and convex subset of the Euclidean space R2 with smooth boundary ∂Ω and suppose that D is the unit disk. Then, given any homeomorphism μ : ∂ D → ∂ Ω, there exists a unique harmonic function u : D → Ω such that u = μ on ∂D and u is a diffeomorphism.

References

Radó's theorem (harmonic functions) Wikipedia


Similar Topics
None Shall Escape
Pastorale heroica
Miki Furukawa
Topics
 
B
i
Link
H2
L