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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characteristic property of Delaunay surfaces
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by Thomas Hasanis and Rafael López PDF
Proc. Amer. Math. Soc. 148 (2020), 5291-5298 Request permission


We prove that Delaunay surfaces, besides the plane and the cate- noid, are the only surfaces in Euclidean space with nonzero constant mean curvature that can be expressed by an implicit equation of type $f(x)+g(y)+h(z)=0$, where $f$, $g$ and $h$ are smooth real functions of one variable.
  • A. Cayley, On a special surface of minimum area, Quart. J. P. Appl. Math. 14 (1877), 190–196.
  • C. Delaunay, Sur la surface de révolution dont la courbure moyenne est constante, J. Math. Pures et Appl. 6 (1841), no. 1, 309–320.
  • Maurice Fréchet, Détermination des surfaces minima du type $a(x)+b(y)=c(z)$, Rend. Circ. Mat. Palermo (2) 5 (1956), 238–259 (1957) (French, with Esperanto summary). MR 87139, DOI 10.1007/BF02849386
  • Maurice Fréchet, Détermination des surfaces minima du type $a(x)+b(y)=c(z)$. II. Quadratures, Rend. Circ. Mat. Palermo (2) 6 (1957), 5–32 (French). MR 95483, DOI 10.1007/BF02848440
  • Huili Liu, Translation surfaces with constant mean curvature in $3$-dimensional spaces, J. Geom. 64 (1999), no. 1-2, 141–149. MR 1675966, DOI 10.1007/BF01229219
  • Johannes C. C. Nitsche, Lectures on minimal surfaces. Vol. 1, Cambridge University Press, Cambridge, 1989. Introduction, fundamentals, geometry and basic boundary value problems; Translated from the German by Jerry M. Feinberg; With a German foreword. MR 1015936
  • H. F. Scherk, Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen, J. Reine Angew. Math. 13 (1835), 185–208 (German). MR 1578041, DOI 10.1515/crll.1835.13.185
  • H. A. Schwarz, Gesammelte mathematische Abhandlungen, 2 vols. Springer, Berlin, 1890. MR0392470 (52 #13287)
  • J. Weingarten, Ueber die durch eine Gleichung der Form $\mathfrak {X}+\mathfrak {Y}+\mathfrak {Z}=0$ darstellbaren Minimalflächen, Nachr. Königl. Ges. d. Wissensch. Univ. Göttingen (1887), 272–275.
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Additional Information
  • Thomas Hasanis
  • Affiliation: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
  • MR Author ID: 82090
  • Email:
  • Rafael López
  • Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
  • ORCID: 0000-0003-3108-7009
  • Email:
  • Received by editor(s): December 9, 2019
  • Received by editor(s) in revised form: February 22, 2020
  • Published electronically: September 4, 2020
  • Additional Notes: The second author was partially supported by the grant no. MTM2017-89677-P, MINECO/AEI/FEDER, UE
  • Communicated by: Jiaping Wang
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 5291-5298
  • MSC (2010): Primary 53A10; Secondary 53C42
  • DOI:
  • MathSciNet review: 4163841