Talk:Conformal radius
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mathworld
[edit]I have just noticed that the mathworld article has nice additional information. It should be incorporated here. --GaborPete (talk) 06:38, 26 January 2010 (UTC)
- OK, I have done that. In fact, it's a slightly different notion of conformal radius, also called logarithmic capacity. Now proper connections with the article capacity of a set should be established. --GaborPete (talk) 08:30, 8 February 2010 (UTC)
Incomplete qualification
[edit]"When D ⊂ C is a connected, simply connected compact set, then its complement E = D^c is a connected, simply connected domain in the Riemann sphere that contains ∞"
This can't quite be right. We need some kind of local path-connectedness, neighborhood retract, or other mild regularity property. Otherwise you can make a loop with the topologist's sine curve that is simply-connected according to the definition, but whose complement is not connected.
2001:171B:2274:7C21:60E8:E9FE:B633:C9CE (talk) 12:22, 5 March 2022 (UTC)
Unclear statement
[edit]The introductory section contains this sentence:
"A closely related notion is the transfinite diameter or (logarithmic) capacity of a compact simply connected set D, which can be considered as the inverse of the conformal radius of the complement E = Dc viewed from infinity."
But the meaning of the word "inverse" here is not clear. Does it mean "reciprocal" ? That word is unambiguous.
I hope someone familiar with this subject will modify that statement so that its meaning becomes clear. ~2026-28336-51 (talk) 18:05, 28 June 2026 (UTC)