## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- Theoretical and Numerical Aspects of Geometric Variational Problems. Gerd Dziuk, Gerhard Huisken, and John Hutchinson, eds. Proceedings of the Centre for Mathematics and its Applications, v. 26. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1991), 201 - 210

### New periodic minimal surfaces in H^3

#### Abstract

We prove existence of new complete embedded minimal surfaces in H3 having the symmetry of a regular tesselation by Coxeter orthoschemes. Each tetrahedron bounds a fundamental piece along four convex symmetry arcs. Its existence is proved by a conjugate surface construction.

#### Article information

**Dates**

First available in Project Euclid:
18 November 2014

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1416323563

**Mathematical Reviews number (MathSciNet)**

MR1139040

**Zentralblatt MATH identifier**

0735.53006

#### Citation

Polthier, Konrad. New periodic minimal surfaces in H^3. Theoretical and Numerical Aspects of Geometric Variational Problems, 201--210, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1991. https://projecteuclid.org/euclid.pcma/1416323563