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1993 A family of singly periodic minimal surfaces invariant under a screw motion
Michael Callahan, David Hoffman, Hermann Karcher
Experiment. Math. 2(3): 157-182 (1993).

Abstract

We construct explicitly, using the generalized Weierstrass representation, a complete embedded minimal surface $M_{k,\theta}$ invariant under a rotation of order $k+1$ and a screw motion of angle $2\theta$ about the same axis, where $k \gt 0$ is any integer and $\theta$ is any angle with $|\theta| \lt \pi/(k+1)$. The existence of such surfaces was proved in [Callahan et al. 1990], but no practical procedure for constructing them was given there.

We also show that the same problem for $\theta=\pm\pi/(k+1)$ does not have a solution enjoying reflective symmetry; the question of the existence of a solution without such symmetry is left open.

Citation

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Michael Callahan. David Hoffman. Hermann Karcher. "A family of singly periodic minimal surfaces invariant under a screw motion." Experiment. Math. 2 (3) 157 - 182, 1993.

Information

Published: 1993
First available in Project Euclid: 3 September 2003

zbMATH: 0807.53004
MathSciNet: MR1273407

Subjects:
Primary: 53A10

Rights: Copyright © 1993 A K Peters, Ltd.

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Vol.2 • No. 3 • 1993
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