A rigidity theorem for Riemann's minimal surfaces
Annales de l'institut Fourier (1993)
- Volume: 43, Issue: 2, page 485-502
- ISSN: 0373-0956
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topRomon, Pascal. "A rigidity theorem for Riemann's minimal surfaces." Annales de l'institut Fourier 43.2 (1993): 485-502. <http://eudml.org/doc/75006>.
@article{Romon1993,
abstract = {We describe first the analytic structure of Riemann’s examples of singly-periodic minimal surfaces; we also characterize them as extensions of minimal annuli bounded by parallel straight lines between parallel planes. We then prove their uniqueness as solutions of the perturbed problem of a punctured annulus, and we present standard methods for determining finite total curvature periodic minimal surfaces and solving the period problems.},
author = {Romon, Pascal},
journal = {Annales de l'institut Fourier},
keywords = {singly-periodic minimal surfaces; minimal annuli; finite total curvature},
language = {eng},
number = {2},
pages = {485-502},
publisher = {Association des Annales de l'Institut Fourier},
title = {A rigidity theorem for Riemann's minimal surfaces},
url = {http://eudml.org/doc/75006},
volume = {43},
year = {1993},
}
TY - JOUR
AU - Romon, Pascal
TI - A rigidity theorem for Riemann's minimal surfaces
JO - Annales de l'institut Fourier
PY - 1993
PB - Association des Annales de l'Institut Fourier
VL - 43
IS - 2
SP - 485
EP - 502
AB - We describe first the analytic structure of Riemann’s examples of singly-periodic minimal surfaces; we also characterize them as extensions of minimal annuli bounded by parallel straight lines between parallel planes. We then prove their uniqueness as solutions of the perturbed problem of a punctured annulus, and we present standard methods for determining finite total curvature periodic minimal surfaces and solving the period problems.
LA - eng
KW - singly-periodic minimal surfaces; minimal annuli; finite total curvature
UR - http://eudml.org/doc/75006
ER -
References
top- [1] M. CALLAHAN, D. HOFFMAN and W. H. MEEKS III, Embedded minimal surfaces with an infinite number of ends, Invent. Math., 96 (1989), 459-505. Zbl0676.53004MR90b:53005
- [2] M. CALLAHAN, D. HOFFMAN and W. H. MEEKS III, The structure of singly-periodic minimal surfaces, Invent. Math., 99 (1990), 455-581. Zbl0695.53005MR92a:53005
- [3] D. HOFFMAN, H. KARCHER and H. ROSENBERG, Embedded minimal annuli in ℝ3 bounded by a pair of straight lines, Comment. Math. Helvetici, 66 (1991), 599-617. Zbl0765.53004MR93d:53012
- [4] L. JORGE and W. H. MEEKS III, The topology of complete minimal surfaces of finite total Gaussian curvature, Topology, Vol 22, no 2 (1983), 203-221. Zbl0517.53008MR84d:53006
- [5] H. KARCHER, Embedded minimal surfaces derived from Scherk's examples, Manuscripta Math., 62 (1988), 83-114. Zbl0658.53006MR89i:53009
- [6] H. KARCHER, Construction of minimal surfaces. Surveys in Geometry, pages 1-96, 1989, University of Tokyo, and Lectures Notes No. 12, SFB256, Bonn, 1989.
- [7] H. B. LAWSON, Lectures on minimal submanifolds, Vol 1, Math-Lectures Series 9, Publish or Perish. Zbl0434.53006
- [8] R. OSSERMAN, A survey of minimal surfaces, Van Nostrand Reinhold Math., 25 (1969). Zbl0209.52901MR41 #934
- [9] J. PÉREZ and A. ROS, Some uniqueness and nonexistence theorems for embedded minimal surfaces. Zbl0789.53004
- [10] B. RIEMANN, Über die Fläche vom kleinsten Inhalt bei gegebener Begrenzung, Abh. Königl., d. Wiss. Göttingen, Mathem. Cl., 13 (1967), 3-52.
- [11] E. TOUBIANA, On the minimal surfaces of Riemann. Zbl0787.53005
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