## JMI2012B-5 Weierstrass representation for semi-discrete minimal surfaces, and comparison of various discretized catenoids (pp.109-118)

Author(s)： Wayne Rossman and Masashi Yasumoto

J. Math-for-Ind. 4B (2012) 109-118.

Abstract
We give a Weierstrass type representation for semi-discrete minimal surfaces in Euclidean $3$-space. We then give explicit parametrizations of various smooth, semi-discrete and fully-discrete catenoids, determined from either variational or integrable systems principles. Finally, we state the shared properties that those various catenoids have.

Keyword(s).　 discrete differential geometry, isothermic surfaces, discrete surfaces, semi-discrete surfaces, minimal surfaces, catenoids, Weierstrass representation