## Experimental Mathematics

- Experiment. Math.
- Volume 6, Issue 1 (1997), 13-32.

### Compact constant mean curvature surfaces with low genus

Karsten Große-Brauckmann and Konrad Polthier

#### Abstract

We describe numerical experiments that suggest the existence of certain new compact surfaces of constant mean curvature. They come in three dihedrally symmetric families, with genus ranging from 3 to 5, 7 to 10, and 3 to 9, respectively; there are further surfaces with the symmetry of the Platonic polyhedra and genera 6, 12, and 30. We use the algorithm of Oberknapp and Polthier, which defines a discrete version of Lawson's conjugate surface method.

#### Article information

**Source**

Experiment. Math., Volume 6, Issue 1 (1997), 13-32.

**Dates**

First available in Project Euclid: 13 March 2003

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1047565281

**Mathematical Reviews number (MathSciNet)**

MR1464579

**Zentralblatt MATH identifier**

0898.53009

**Subjects**

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

Secondary: 49Q05: Minimal surfaces [See also 53A10, 58E12]

#### Citation

Große-Brauckmann, Karsten; Polthier, Konrad. Compact constant mean curvature surfaces with low genus. Experiment. Math. 6 (1997), no. 1, 13--32. https://projecteuclid.org/euclid.em/1047565281