On Alfred Gray's elliptic catenoid.
by
Santiago López-de-Medrano
Universidad Nacional Autónoma de México.
Coauthors: Hugo Jiménez Pérez (Universidad Nacional Autónoma de México)

Oral Communication

The minimal surface obtained by solving Björling's problem for the ellipse was called by Alfred Gray the elliptic catenoid and some pictures of this surface were produced by him using Mathematica. But Mathematica does not seem to be able to deal with multivalued integrals of complex functions and this fact produces mistakes in the pictures so obtained once a singularity of the integrand is passed.

In this talk we solve this problem using elliptic functions, we obtain the correct picture of the elliptic catenoid and we discuss the curves that appear as geodesics to this surface orthogonal to the ellipse at its vertices.

We consider also the corresponding problem for the hyperbola.

Date received: April 11, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadq-28.