Where Can I Find a Simpler Proof of the Riemann Mapping Theorem?

In summary, the conversation is about finding a proof of the Riemann mapping theorem, which the person believes has multiple proofs and the original one is difficult. They are looking for a simpler proof and are suggested to search on Google or go to a library for math books. Someone recommends books by Henri Cartan and Hille on complex analysis and analytic functions. The person thanks them for the help and is advised to use Google as a resource.
  • #1
Zaare
54
0
I'm looking for a proof of the Riemann mapping theorem. If I'm not mistaking, there are differnet proofs and the original proof is quite difficult.
I'd appreciate any information on where I can/might find a less complicated proof of this theorem.
 
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  • #2
Best way to find proofs is just to go to google and type in:

"Riemann mapping theorem" proof

you'll have to sort through a lot of sites but that's probably your best bet. Or you could be old fashioned and actually go to a library and check out the math books...of course that depends on whether or not you have a good math library near you.
 
  • #3
That actually worked, can't believe I didn't think of that myself.
Thanks for the help.
 
  • #4
i recommend henri cartans book on complex analysis, analytic functions of one and several,complex variables. also hille's book on analytic functions, in 2 volumes.
 
  • #5
Zaare said:
That actually worked, can't believe I didn't think of that myself.
Thanks for the help.
no problem

google is your best friend
 

Related to Where Can I Find a Simpler Proof of the Riemann Mapping Theorem?

1. What is the Riemann mapping theorem?

The Riemann mapping theorem is a fundamental result in complex analysis that states that any simply connected open subset of the complex plane can be conformally mapped onto the unit disk in the complex plane.

2. Who discovered the Riemann mapping theorem?

The Riemann mapping theorem was first proved by the German mathematician Bernhard Riemann in 1851.

3. What is the significance of the Riemann mapping theorem?

The Riemann mapping theorem is significant because it provides a way to map any simply connected domain in the complex plane to the unit disk, which is a more manageable and well-studied domain. This allows for easier analysis and computation of complex functions.

4. What are some applications of the Riemann mapping theorem?

The Riemann mapping theorem has many applications in mathematics and physics, including in the study of conformal mappings, potential theory, and fluid dynamics. It also has practical applications in engineering and technology, such as in the design of electrical circuits and in computer graphics.

5. Are there any generalizations of the Riemann mapping theorem?

Yes, there are several generalizations of the Riemann mapping theorem, including the Ahlfors-Beurling extension theorem, which extends the theorem to non-simply connected domains, and the Uniformization theorem, which extends the theorem to Riemann surfaces.

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