BYU

Abstract by Spencer Taylor

Personal Infomation


Presenter's Name

Spencer Taylor

Degree Level

Undergraduate

Co-Authors

Gary Lawlor

Abstract Infomation


Department

Mathematics

Faculty Advisor

Gary Lawlor

Title

The Triple Spatial Bubble Problem in R^3

Abstract

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.