bio | website | pcwww.liv.ac.uk/~lrempe |
---|---|---|
location | Liverpool | |
age | 37 | |
visits | member for | 5 years, 5 months |
seen | yesterday | |
stats | profile views | 997 |
Professor of Pure Mathematics at the University of Liverpool
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 |
Anti-Mandelbrot set
Higher-degree (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 non-rational 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 Caratheodory-Torhorst 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 Caratheodory-Torhorst 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 Caratheodory-Torhorst 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 | Non-bijective conformal maps between annuli |
May 22 |
revised |
Conformal map and Jordan curve
Provided further details for the argument and adjusted notation. |
May 22 |
comment |
Conformal map and Jordan curve
No. If you look carefully, the curve $\gamma$ itself is analytic. I shall see whether I can clarify the answer. |
May 22 |
comment |
A Generalization of growth exponents
@Catman You might wish to post another question, giving all the details. (You could then post a link here if you wish.) |
May 22 |
answered | Conformal map and Jordan curve |
May 20 |
answered | A Generalization of growth exponents |
May 19 |
comment |
A Generalization of growth exponents
This is clearly not continuous, unless I am missing something. E.g. consider $f(s,a):= a\cdot s^2$, at $a=0$. |