1,629 reputation
716
bio website pcwww.liv.ac.uk/~lrempe
location Liverpool
age 36
visits member for 4 years, 5 months
seen Jul 20 at 21:47
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