Talk:Quasicircle

Characterisation

So what is objectionable about the result of Blevins and Palka? Ansatz (talk) 21:21, 21 December 2011 (UTC)

You wrote, "A quasicircle may also be characterised as a Jordan curve which is set-wise invariant under a quasiconformal mapping."

That statement is false, misleading and not even remotely close to what was written in the abstract. You were unable to spot that the statement generalized well known properties of conformal transformations on the sphere that leave a given circle invariant.

Beyond that, this well trodden hoary subject is covered in numerous text books on both Teichmüller theory and complex dynamical systems. The normal process in editing mathematics articles is to use secondary sources, in this case established textbooks. I found almost no hint of that in what you wrote, only complete howlers and randomly chosen results from a vast literature.

One interesting thing about the sentence you added is the British spelling. Probably the best place to explain yourself is at the latest SPI report I filed concerning your account at Wikipedia:Sockpuppet investigations/Echigo mole. Mathsci (talk) 22:49, 21 December 2011 (UTC)

The condition in the paper is that "given ordered triples z1,z2,z3 and w1,w2,w3 of points on Gamma there exists a K-quasiconformal mapping h of C bar onto itself with h(Gamma) = Gamma and h(zj) = wj for j=1,2,3" The version I gave is a simplified rendition into plain -- or at least, mathematical -- English, deliberately omitting the triple transitivity condition for simplicity. There was a full citation and a link to an online version of the original paper for anyone interested to see the exact condition. This does not seem to be a reason for removing it, and of course anyone can improve it if they wish.

Not giving the full context in the theory of conformal and quasiconformal maps is more a matter of time than competence but again anyone who sees it as a major defect is welcome to add the material themselves. Context and characterisation are not the same thing, and lack of one is not a reason to remove the other.

British English spelling is perfectly acceptable on Wikipedia. Ansatz (talk) 07:47, 22 December 2011 (UTC)

I'm sorry, this reply with its inadequate excuses appears to be trolling. Not even a starting graduate student in mathematics would omit a simple mathematical condition that is easy to state. (Your "simplified definition" makes any Jordan curve a quasicircle; apart from being wrong in a mathematically naive way, your edit fails WP:V). But this particular result that you decided was important is clearly WP:UNDUE. It is published in a minor journal and does not figure in the main text books on the subject, of which there are many. You are using primary sources and writng a personal essay, so WP:SYNTH, WP:OR, WP:POV, etc. This is just one of a series of undergraduate howlers and misconceptions which plague your edits. The same was true of the edits of Julian Birdbath and A.K.Nole, whose editing various arbitrators described charitably as "mathematically naive". The best place to explain why you are editing in this extraordinary way is the SPI report. Mathsci (talk) 08:40, 22 December 2011 (UTC)

Whether or not this characterisation was given undue weight is of course a matter of opinion, and it would have been easy to say so from the beginning, without the acrimonious personal comments. Proceedings of the American Mathematical Society ishardly a minor journal, though. Whether, and how, to give the gist of a piece of mathematics is a matter of style, but it is fair to say that phrases like "roughly speaking", for example, should be used to signal the difference from formal mathmatical exposition. Ansatz (talk) 09:11, 22 December 2011 (UTC)

Proceedings of the AMS is for short notes, transactions for longer articles and the journal of the AMS is the high level journal. Prestigious journals are Annals, Acta, Inventiones, etc. But please leave your comments at the SPI report. Apart from A.K.Nole, Zarboublian and Julian Birdbath, it's rare to find people trolling on specialist mathematics articles. Mathsci (talk) 10:48, 22 December 2011 (UTC)

links to this article

I've added this article to the list of circle topics, but otherwise no other articles link to it. Appropriate links from other articles should be added. Michael Hardy (talk) 04:43, 22 December 2011 (UTC)

There was a link at Grunsky matrix but the author decided to remove it. Ansatz (talk) 07:48, 22 December 2011 (UTC)

It was an unnecesssary side remark. As indicated at the top of the page, the first version of the article is still being written; that involves lots of side articles, some elementary, some less so. The model of universal Teichmüller space that occurs in the theory does not involve general quasicircles and indeed no general theory of Cauchy singular integral operators has been developed on an arbitrary quasicircle. Mathsci (talk) 09:45, 22 December 2011 (UTC)

Quasiconformal curve

The phrase is used as a synonym for quasicircle in Andrievski & Blatt, Discrepancy of signed measures and polynomial approximation; Becker, Holder continuity of conformal mappings ...; Lesley, A non-quasi-circle with almost smooth mapping function; and by Pommerenke and Jensen, Univalent functions p.286, first sentence of section 9.4. Ansatz (talk) 09:21, 22 December 2011 (UTC)

The term is used at length in the 1973 classic by Lehto and Virtanen, but also in connection with Jordan arcs. Pommerenke's book is not on quasiconformal mappings: on the few occasions they are needed, he usually refers to the book of Lehto and Virtanen. Pommerenke discusses quasicircles only in connection with the Grunsky matrix, which seems to be your main centre of interest on wikipedia. The term was dropped by Lehto in his 1987 book on Univalent functions and Teichmuller theory in favour of quasicircle: there is also the notion of quasidisc. On page 38 of Lehto's book, where both terms are defined, more can be found on quasicircles than you succeeded in adding to this article. Lehto includes a reference to complex dynamical systems where quasicircles appear as Julia sets. Unless you are a graduate student in mathematics or beyond, I don't understand how you can even begin to edit articles like this. You wrote something which implied that every Jordan curve is a quasicircle and thought that was fine. But it is not fine. Nor for that matter is wikistalking or sockpuppetry. Mathsci (talk) 10:41, 22 December 2011 (UTC)

I agree that quasiconformal curve was also used, but less often, as referring to an image of an arc or line segment. By why say "in German"? The sources I gave are in English. However, glad to see you agree with me that it needs to be mentioned as something that someone might look up in an encyclopaedia. We thrashed out the "every Jordan curve is a quasicircle" thing in another section, why not keep the discussion in one place. Ansatz (talk) 12:13, 22 December 2011 (UTC)