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

Assume that $f$ is (Euclidean) $L-$biLipchitz mapping of the unit circle onto a triangle $\Delta(A,B,C)$. Can we find a $10000 L$ bi-lipchitz extension of $f$ onto the whole plane.

share|improve this question

1 Answer 1

See http://arxiv.org/pdf/1203.3443.pdf: The results of the paper are for maps $R\to R^2$, but, as the author says in the introduction, conjugating with Moebius transformations, one gets bi-Lipschitz extension for maps of the unit circle (with controlled increase in the BL-constant). Now, you would have to do some computations yourself to see if the constant you get is $<10^4$.

Edit: Here is the full statement of Kovalev's theorem I linked above, since it is very nice and deserves to be better known:

Let $f: {\mathbb R}\to {\mathbb R}^2$ be an $L$-bi-Lipschitz embedding. Then $f$ extends to an $2000L$-bi-Lipschitz embedding ${\mathbb R}^2\to {\mathbb R}^2$.

Unfortunately, the result is not quite what you need.

share|improve this answer
    
Then you obtain $L^9$ growth of bi-Lipschitz constant. –  djoke May 21 '13 at 6:34

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.