Abstract by Darian Comsa
Tying Down the Computer-Assisted Triple Bubble Proof
It has not been proven in three dimensions that the standard triple bubble has minimal surface area for three equal volumes. Real world bubbles mostly deal with more than one volume and the solution to minimizing the surface area is handled flawlessly by the natural world. The mathematics behind the simple sphere are complicated and lead to diverse questions involving higher-dimensional volumes and boundaries. Our work has focused on helping to develop and prove lemmas concerning curvature, centroid position, weighted perimeter inequalities, and the states of planar sections by analyzing Möbius transformations of planar sections of the triple bubble, which are used to reduce the minimizer cases to computational shapes. The use of interval calculus on two-dimensional slices provides the flexibility of computation for changes in surface area to be accurately measured.