Complete minimal surfaces of arbitrary genus in a slab of ℝ 3

Celso J. Costa; Plinio A. Q. Simöes

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 2, page 535-546
  • ISSN: 0373-0956

Abstract

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In this paper we construct complete minimal surfaces of arbitrary genus in ℝ 3 with one, two, three and four ends respectively. Furthermore the surfaces lie between two parallel planes of ℝ 3 .

How to cite

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Costa, Celso J., and Simöes, Plinio A. Q.. "Complete minimal surfaces of arbitrary genus in a slab of ${\mathbb {R}}^3$." Annales de l'institut Fourier 46.2 (1996): 535-546. <http://eudml.org/doc/75187>.

@article{Costa1996,
abstract = {In this paper we construct complete minimal surfaces of arbitrary genus in $\{\Bbb R\}^3$ with one, two, three and four ends respectively. Furthermore the surfaces lie between two parallel planes of $\{\Bbb R\}^3$.},
author = {Costa, Celso J., Simöes, Plinio A. Q.},
journal = {Annales de l'institut Fourier},
keywords = {minimal surfaces; Weierstrass representation; lacunary series},
language = {eng},
number = {2},
pages = {535-546},
publisher = {Association des Annales de l'Institut Fourier},
title = {Complete minimal surfaces of arbitrary genus in a slab of $\{\mathbb \{R\}\}^3$},
url = {http://eudml.org/doc/75187},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Costa, Celso J.
AU - Simöes, Plinio A. Q.
TI - Complete minimal surfaces of arbitrary genus in a slab of ${\mathbb {R}}^3$
JO - Annales de l'institut Fourier
PY - 1996
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 2
SP - 535
EP - 546
AB - In this paper we construct complete minimal surfaces of arbitrary genus in ${\Bbb R}^3$ with one, two, three and four ends respectively. Furthermore the surfaces lie between two parallel planes of ${\Bbb R}^3$.
LA - eng
KW - minimal surfaces; Weierstrass representation; lacunary series
UR - http://eudml.org/doc/75187
ER -

References

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  1. [1] F.F. BRITO, Power series with Hadamard gaps and hyperbolic complete minimal surfaces, Duke Math. Journal, 68 (1993), 297-300. Zbl0787.53007MR94d:53012
  2. [2] L.P.M. JORGE and F. XAVIER, A complete minimal surfaces in R3 between two parallel planes, Ann. Math., 112 (1980), 203-206. Zbl0455.53004MR82e:53087
  3. [3] F.R. LOPEZ, A non orientable complete minimal surfaces in R3 between two parallel planes, Proc. Am. Math. Soc., 103 (1988). Zbl0662.53008MR89f:53009
  4. [4] R. OSSERMAN, A survey of minimal surfaces, Van Nostrand, New York, 1969. Zbl0209.52901MR41 #934
  5. [5] H. ROSENBERG and E. TOUBIANA, A cylindrical type complete minimal surfaces in a slab of R3, Bull. Sc. Math., III (1987), 241-245. Zbl0631.53012MR88k:53019
  6. [6] A. ZYGMUND, Trigonometric series, Cambridge University Press, New York, 1968. 

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