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

An immersed surface becomes singular

(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 17 minutes.


After 0 time steps.
after 0 steps
After 5,000 time steps.
after 5,000 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 200,000 time steps.
after 200,000 steps

After 300,000 time steps.
after 300,000 steps
After 450,000 time steps.
after 450,000 steps

After 600,000 time steps.
after 600,000 steps
After 680,000 time steps.
after 680,000 steps
[leftarrow] Back mayer@math.utah.edu
Posted on: Tue Apr 10 12:05:38 PDT 2001