bio  website  pcwww.liv.ac.uk/~lrempe 

location  Liverpool  
age  37  
visits  member for  5 years, 6 months 
seen  yesterday  
stats  profile views  1,007 
Professor of Pure Mathematics at the University of Liverpool
1d

answered  A question on $J(f)$ and $J(f')$ 
Jul 16 
comment 
Growth of the size of iterated polynomials
I am a little confused  but may have missed some subtlety. 1) Should $\log$ not be $\log_+$ (i.e., maximum of 0 and the logarithm)? Otherwise, what happens for $p(z)=z^2$ and $a=0$? 2) If this is the case, why isn't the convergence a consequence of [the proof of] Boettcher's theorem? 
Jul 13 
revised 
Do the bounded isophase lines of a complex polynomial $f$ through the zeroes of $f’$ define a spanning tree?
added 1037 characters in body 
Jul 13 
comment 
Do the bounded isophase lines of a complex polynomial $f$ through the zeroes of $f’$ define a spanning tree?
Ah, this is essentially the same as Alex's corrected answer (which was not there when I started typing mine). I will leave it because maybe there are some additional details that might be helpful. 
Jul 13 
answered  Do the bounded isophase lines of a complex polynomial $f$ through the zeroes of $f’$ define a spanning tree? 
Jul 1 
comment 
Is Every Holomorphic Near an Entire?
In addition to the answers given, a literature reference: Dieter Gaier, "Lectures on Complex Approximation", includes Mergelyan's and Arakelyan's theorems, and much more! 
Jun 12 
answered  Equivalence of Definitions of Quasiconformal Surfaces? 
Jun 8 
revised 
Can the image of a disk have nontrivial Hausdorff measure for $1 < d < 2$?
added 75 characters in body 
Jun 8 
answered  Can the image of a disk have nontrivial Hausdorff measure for $1 < d < 2$? 
Jun 8 
comment 
AntiMandelbrot set
Higherdegree (unicritical) versions are sometimes called "multicorns". I believe Dierk Schleicher is among the people who has done some work on the topic (after Milnor). 
Jun 5 
comment 
Fixed point property for intersection of spaces which are homeomorphic to a disk
I think you mean "does not separate the plane" in the Question. 
Jun 2 
comment 
Is this a rational function?
Any globally defined meromorphic function that has a removable singularity (as a function on the Riemann sphere) at $\infty$ is clearly rational. Hence any nonrational meromorphic function in the plane has an essential singularity at infinity, and is transcendental. 
Jun 1 
comment 
Is this a rational function?
@GeraldEdgar  surely this follows also from the first argument given in this answer? Indeed, any globally defined meromorphic function is either rational or transcendental. 
May 26 
awarded  Nice Question 
May 24 
revised 
Continuous extension of Riemann maps and the CaratheodoryTorhorst Theorem
clarified what is and is not statedin Torhorst's paper. Also added link for Wilder's paper. 
May 23 
comment 
Continuous extension of Riemann maps and the CaratheodoryTorhorst Theorem
Not sure if Torhorst explicitly mentions continuous extension but this is clearly understood. Will try to clarify in question when I get the chance. 
May 23 
comment 
Continuous extension of Riemann maps and the CaratheodoryTorhorst Theorem
Thanks for the interest. Posting from mobile so apologies for typos. 1. Carathéodory considered SIMPLE closed curves, not general curves. 2. Carathéodory proves continuous extension iff all prime ends of first kind. Torhorst proves and states all prime ends of first kind iff lc. 
May 22 
awarded  Promoter 
May 22 
answered  Nonbijective conformal maps between annuli 
May 22 
revised 
Conformal map and Jordan curve
Provided further details for the argument and adjusted notation. 