Knot energies
What is the nicest shape of a knot - and how to find it!
Simply speaking, this project deals with the following three questions:
- What is the nicest shape of a knot?
- How nice are these nicest shapes?
- Are there ways (evolution equations, algorithms) to transform a give geometric knot into its nicest shape?
Have a look at the following amazing videos of Keenan Crane to get a feeling of what this can be used for. There is a short introductory one on curves and a complete lecture dealing with topologically complicated surfaces. You can find a lot of other interesting stuff on Keenan’s youtube chanel and homepage.