Frank Morgan

In a talk at Columbia University today (April 15, 2022), Gary Lawlor announced and described his proof that the standard triple soap bubble in R^3 is the least-perimeter way to enclose and separate three equal volumes.

Update 5/19/22: Milman and Neeman post proof of general triple and quadruple bubble conjectures in R^n and S^n https://arxiv.org/abs/2205.09102. See my review at https://amathr.org/milman-and-neeman and the beautiful Quanta article by Erica Klarreich.

Update 7/18/23: Milman and Neeman post proof of quintuple bubble conjecture as promised https://arxiv.org/abs/2307.08164.