Abstract
The work is concerned with a special family of axially symmetric surfaces providing local extrema to the so-called Willmore functional, which assigns to each surface its total squared mean curvature. The components of the position vector of the profile curves of the regarded Willmore surfaces satisfy a system of first-order ordinary differential equations. The solutions of this system are expressed by quadratures in terms of the tangent angle and, in this way, the corresponding Willmore surfaces are determined.
Information
Digital Object Identifier: 10.7546/giq-17-2016-369-378