Journal of Undergraduate Research
Keywords
planar equitent conjecture, isoperimetry, minimal surfaces
College
Physical and Mathematical Sciences
Department
Mathematics
Abstract
The goal of this project was to explore a new problem in geometric optimization: isoperimetric surfaces with both boundary and volume constraints. The idea behind the problem is the following: what is the optimal way to enclose a given volume with a surface that must also span a given boundary? In this case, optimal means least possible surface area. If we were to consider only the volume constraint, we would have the classical isoperimetric problem—and by now it is well-known and mathematically proven that the best way to enclose a given volume is with a sphere. On the other hand, by considering only the boundary conditions, we find ourselves in the territory of minimal surface theory and the Steiner problem.
Recommended Citation
Frandsen, Abraham and Dorff, Dr. Michael
(2013)
"The Planar Equitent Conjecture: Combining Isoperimetry and Minimal Surfaces,"
Journal of Undergraduate Research: Vol. 2013:
Iss.
1, Article 2705.
Available at:
https://scholarsarchive.byu.edu/jur/vol2013/iss1/2705