Ironically this donut shaped coffee cup is now no longer topologically similar to a donut!
pic.twitter.com/jQXCDQEnwQ
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Ironically this donut shaped coffee cup is now no longer topologically similar to a donut!
pic.twitter.com/jQXCDQEnwQ
Would be nice to see how this shape evolves under Willmore flow! like the one you did with @henryseg for the genus 1 version:https://www.youtube.com/watch?v=9NlqYr6-TpA …
minimial willmore surfaces are an open problem in higher genus but this is likely to flow to (a Moebius equivalent to) an "eight" shape.
This is genus 3 though? I'd be interested to see that flow. Also I still get confused by the difference between Willmore surfaces and CMC surfaces.
The conjectured minimizers of the Willmore energy are "Lawson surfaces". Lots of nice pictures in this paper of Hsu, Kusner and Sullivan: https://projecteuclid.org/euclid.em/1048622023 … Here's a polyhedron with genus 3 flowing towards a discrete approximation of a Lawson surface.pic.twitter.com/OPIPLeSHRl
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