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WILMORE'S TORUS


Links:
Wikipedia article on the Willmore conjecture
www.chem.ucla.edu/~michalet/papers/larecherche/f-tores.html
torus.math.uiuc.edu/jms/Images/will.html

Willmore's torus is the torus for which the ratio of the major and minor axes is equal to . Willmore conjectured in 1965 that it is the orientable surface of genus 1 with an axis of symmetry that has the minimum curvature energy possible (conjecture proved in 2014). The other ones are the inverses of this torus, i.e. special Dupin cyclides.
This was verified through experimentation by the shapes assumed by liposomes.
 
 
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© Robert FERRÉOL  2017