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Rado's theorem
In mathematics, Rado's theorem is a result about harmonic functions. 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
R. Schoen, S. T. Yau. (1997) Lectures on Harmonic Maps. International Press, Inc., Boston, Massachusetts. ISBN 1-57146-002-0.
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details