Willmore flow for the radially symmetric case in in three space dimensions

A torus evolves into a stationary Willmore torus

(Graphics show half of the surface of revolution)
Scale: Major radius = 5, minor radius = 2.
Time step = 10-3.
Spatial resolution of generating curve = 0.01-0.05.
System: Toshiba 4015CDT Laptop with an Intel Pentium II 266 MHz.
Computation time: About 53 minutes.


After 0 time steps.
After 3,000 time steps.

After 10,000 time steps.
After 25,000 time steps.

After 50,000 time steps.
After 100,000 time steps.

After 500,000 time steps.
After 1,500,000 time steps.
[leftarrow]Back mayer@math.utah.edu
Posted on: Tue Apr 10 12:05:38 PDT 2001