Willmore Surface Images

Copyright by John M. Sullivan

http://www.math.uiuc.edu/~jms
jms@math.uiuc.edu

Back to my other Mathematical Images.
See also photographs I took of Tom Willmore and other mathematicians standing next to the Willmore/Boy's surface sculpture at Oberwolfach.
The Willmore bending energy of a surface is the integral (over that surface) of squared mean curvature. A Willmore surface is a minimum (or any critical point) for this energy. One way to get a Willmore surface (in R^3) is to stereographically project a minimal surface in S^3. The two surfaces pictured here arise in this way from a pair of conjugate minimal surfaces in S^3.