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

An immersed surface stays regular

(Graphics show half of the surface of revolution)
Scale: Major radius = 2, minor radius = 1.
Time step = 10-5.
Spatial resolution of generating curve = 0.01-0.05.
System: Toshiba 4015CDT Laptop with an Intel Pentium II 266 MHz.
Computation time: About 1 hours, 44 minutes.


After 0 time steps.
after 0 steps
After 25,000 time steps.
after 25,000 steps

After 75,000 time steps.
after 75,000 steps
After 200,000 time steps.
after 200,000 steps

After 350,000 time steps.
after 350,000 steps
After 500,000 time steps.
after 500,000 steps

After 750,000 time steps.
after 750,000 steps
After 1,000,000 time steps.
after 1000,000 steps

After 1,500,000 time steps.
after 1500,000 steps
After 5,000,000 time steps.
after 5000,000 steps
[leftarrow]Back mayer@math.utah.edu
Posted on: Tue Apr 10 12:05:38 PDT 2001