Timeline for answer to Tweetable way to see that Willmore energy is Möbius invariant? by Yuri Vyatkin

7 events

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Jun 16, 2012 at 22:08	comment	added	Glen Wheeler		The Willmore energy is not invariant under inversions centred at some point on the image -- this is well-known. Some energy is lost depending on density. Similarly, images which stretch off to infinity gain energy under inversion.
Jun 15, 2012 at 20:20	comment	added	Sebastian		@Will, fuzzytron. It is even true for conformal changes of the metric, not only Moebius transformations, as was shown in "Weiner, J., (1978) On a problem of Chen, Willmore, et al., Indiana University Mathematical Journal."
Jun 15, 2012 at 3:46	comment	added	Will Jagy		@fuzzytron, conformal transformations of $\mathbb R^3.$ These come from stereographic projection to $\mathbb S^3,$ some isometry there, then stereographic projection back.
Jun 14, 2012 at 22:26	history	edited	Yuri Vyatkin	CC BY-SA 3.0	fixed another typo
Jun 14, 2012 at 22:20	history	edited	Yuri Vyatkin	CC BY-SA 3.0	Corrected minor typos; added an edit to address the comments.
Jun 14, 2012 at 16:07	comment	added	TerronaBell		Something is not quite right here - you would claim that Willmore energy is not only Möbius invariant but actually conformally invariant? But that is not true - consider two different conformal immersions of the sphere. They will not in general have the same Willmore energy, but one is certainly a conformal transformation of the other since there is only one conformal structure on $S^2$.
Jun 14, 2012 at 11:59	history	answered	Yuri Vyatkin	CC BY-SA 3.0