International Workshop on Geometry and Interfaces
J. Phys. Colloques 51 (1990) C7-149-C7-156
DOI: 10.1051/jphyscol:1990714
WEIERSTRASS REPRESENTATION OF PERIODIC MINIMAL SURFACES
A. FOGDENDepartment of Applied Mathematics, Research School of Physical Sciences, Australian National University, GPO Box 4, Canberra 2601, Australia
Abstract
A general algorithm for the construction of infinite periodic minimal surfaces (IPMS) via their Weierstrass function is outlined, enabling parameterisation of known examples, and forming the bases of a systematic search for all such surfaces. For the 'regular' class of IPMS (including the low genus surfaces) the Weierstrass function has a simple form, permitting a complete listing of all possibilities. The method is then readily extended to parametrisation of the 'irregular' class of IPMS, and its generally illustrated with several previously unsolved examples.
© EDP Sciences 1990