Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

How can one show that rational functions satisfy a Lipschitz condition in the chordal metric on the Riemann sphere?

share|improve this question

1 Answer 1

up vote 2 down vote accepted

By compactness, you only need to prove the Lipschitz property locally. First prove that Möbius transforms are Lipschitz (easy – they are compositions of translations, multiplications by constants, and inversions). Then, by composing with suitable Möbius transforms, you only need to show that a rational function which maps 0 to 0 is Lipshitz on a neighbourhood of 0. This is trivial, I hope you agree.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.