bio | website | pcwww.liv.ac.uk/~lrempe |
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location | Liverpool | |
age | 36 | |
visits | member for | 4 years, 5 months |
seen | Jul 20 at 21:47 | |
stats | profile views | 848 |
Professor of Pure Mathematics at the University of Liverpool
Jul 2 |
awarded | Curious |
Jun 23 |
answered | Is there a effective computational criterion to all periodic points of a rational function are repelling. |
Jun 9 |
answered | existence of rational functions with prescribed critical values and ramification degrees at critical points |
May 25 |
comment |
Original article about a theorem of Cartan on iterations of analytic functions
If you are looking for a generalization in complex dimension 1, then this is given by the (hyperbolic version of) the Schwarz lemma. |
May 25 |
comment |
Original article about a theorem of Cartan on iterations of analytic functions
As stated in my answer, if you are looking for the theorem that you state, this is the Schwarz lemma, via covering theory. |
May 12 |
answered | Original article about a theorem of Cartan on iterations of analytic functions |
May 12 |
revised |
Original article about a theorem of Cartan on iterations of analytic functions
Corrected the statement (f(a) should be f'(a)). Also changed the statement slightly, since edits must be at least 6 characters. |
May 12 |
comment |
Original article about a theorem of Cartan on iterations of analytic functions
This statement is known as the Schwarz lemma in the case of the disc, and Pick's Theorem or the Schwarz-Pick Lemma when transferred to the hyperbolic metric of general domains. (Here there isn't the assumption that a is fixed, and the conclusion in 2) being that f is a covering map. Your statement follows from this version.) Unfortunately I can't say that I really know the history of the statement. On what basis do you think it should have been first stated in this form by Cartan? |
May 12 |
suggested | suggested edit on Original article about a theorem of Cartan on iterations of analytic functions |
May 4 |
comment |
Bounds on the derivative of a Riemann map
James: It seems like a slightly odd (by which I mean not very natural-looking) question. For example, if your domain has Dini-smooth boundary, then the derivative will extend continuously to the boundary. Hence a sufficiently small rescaling of your domain will satisfy your condition. Potentially you could get something out of this by looking at the constants, but somehow I doubt it will be very nice. What applications do you have in mind? |
Apr 28 |
revised |
Beautiful examples of arc-like continua
Added link to preprint |
Apr 14 |
comment |
A question for hyperbolic metric in the proof for Bohr's lemma
I suspect that for 'on the boundary' you might want to read 'in the complement'. |
Apr 13 |
comment |
13 months and not even one report. what would you do?
Good to hear that there has finally been some progress. Hopefully this whole experience will be over for you soon. |
Apr 13 |
answered | A question for hyperbolic metric in the proof for Bohr's lemma |
Apr 13 |
awarded | Revival |
Feb 22 |
awarded | Enlightened |
Feb 22 |
awarded | Nice Answer |
Feb 8 |
answered | Extending a function from $\mathbb{Q}$ to the upper half plane $\mathbb{H}\cup\mathbb{Q}\cup\{i\infty\}$ |
Jan 30 |
awarded | Yearling |
Dec 11 |
accepted | Belyi functions on non-compact surfaces; or: Building Riemann surfaces from equilateral triangles |