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

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

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

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