Proceedings of the Centre for Mathematics and its Applications

New periodic minimal surfaces in H^3

Konrad Polthier

Full-text: Open access

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

Source
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

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


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