- Minimal Spheres in Ellipsoids
- Project Year:
2020
- REU Student (s):
Ezra Seidel | Rutgers University-New Brunswick NJ
- Student 1 Institution:
Rutgers University-New Brunswick
- Project Mentor:
Daniel Ketover
- Project Mentor Area:
Mathematics
- Project Abstract:
It is known result in differential geometry that a 3-ellipsoid which is near spherical contains 4 minimal 2-spheres, and that if the 3-ellipsoid is scaled enough along one axis, additional minimal 2-spheres occur. We attempt to show that as this scaling approaches infinity, in other words, as the 3-ellipsoid approaches a higher dimensional cylinder, the number of minimal 2-spheres approaches infinity. The method we use is to take advantage of the rotational symmetry of an ellipsoid to reduce the problem to finding geodesics in a two-dimensional metric space, which can be done by finding the solutions to a system of nonlinear ordinary differential equations.
