Rado’s theorem
Theorem (Rado).
Suppose is a convex (http://planetmath.org/ConvexSet) domain (http://planetmath.org/Domain2) with a smooth boundary and suppose that is the unit disc. Then given any homeomorphism , there exists a unique harmonic function such that on and is a diffeomorphism
.
References
- 1 R. Schoen, S. T. Yau. . International Press, Inc., Boston, Massachusetts, 1997