Abstract by Spencer Taylor
The Triple Spatial Bubble Problem in R^3
This is an important open problem in mathematics that concerns proving that the minimal closed surface containing three equal volumes in R^3 is a standard triple bubble. The approach that we take in tackling this problem is by considering "competitors" to our proposed minimizer and comparing weighted areas and perimeters of cross-sectional slices. This requires using tools and techniques from a vast variety of mathematical fields, including geometric measure theory, group theory, graph theory, interval analysis, differential geometry of curves and surfaces, and more. Applications of understanding the triple bubble and other minimal surfaces of are diverse and range from molecular engineering and materials science to the apparent horizon problem in general relativity.