Timeline for What is combinatorially possible, for a singular minimal surface in $\mathbf{R}^3$?
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| Jul 23, 2016 at 16:14 | comment | added | David Treumann | Hi Ian. I'd be just as interested to find out there are combinatorial restrictions on foam with nonsimply-connected bubbles. But the actual question that came up for me is even more restricted: if you draw a cubic planar graph on the boundary of a ball, what kind of minimal surfaces, with Plateau singularities and without interior regions, can you fill inside? | |
| Jul 23, 2016 at 15:19 | comment | added | Ian Agol | Can you clarify, are you allowing the faces and regions of the soap bubbles to be non-simply connected? For example there are (unstable) toroidal double bubbles satisfying Plateau's laws. One can form a dual complex abstractly, but it might not be a triangulation of S^3 (for example, there may be no vertices). torus.math.uiuc.edu/jms/Images/double | |
| Jul 23, 2016 at 14:55 | history | asked | David Treumann | CC BY-SA 3.0 |