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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stable periodic projective planes


Author: Manuel Ritoré
Journal: Proc. Amer. Math. Soc. 124 (1996), 3851-3856
MSC (1991): Primary 53A10; Secondary 49Q20
MathSciNet review: 1363182
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Abstract: We find all stable projective planes with finite topology which are properly embedded in $\Bbb R^3/\varGamma $, where $\varGamma $ is a discrete subgroup of translations in $\Bbb R^3$. Here stable means second order minimum of the area. The surfaces we obtain are a quotient of the helicoid and quotients of the doubly periodic Scherk surfaces.


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Additional Information

Manuel Ritoré
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, E–18071, Granada, Spain
Email: ritore@goliat.ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03681-7
PII: S 0002-9939(96)03681-7
Keywords: Minimal surfaces, stable surfaces
Received by editor(s): June 12, 1995
Additional Notes: Research partially supported by DGICYT grant PB94–0796
Communicated by: Peter Li
Article copyright: © Copyright 1996 American Mathematical Society