Open Access
Mar 2005 The classification of doubly periodic minimal tori with parallel ends
Joaquín Pérez, M. Magdalena Rodríguez, Martin Traizet
J. Differential Geom. 69(3): 523-577 (Mar 2005). DOI: 10.4310/jdg/1122493998


Let 𝒦 be the space of properly embedded minimal tori in quotients of ℝ3 by two independent translations, with any fixed (even) number of parallel ends. After an appropriate normalization, we prove that 𝒦 is a 3-dimensional real analytic manifold that reduces to the finite coverings of the examples defined by Karcher, Meeks and Rosenberg in [9, 10, 15]. The degenerate limits of surfaces in 𝒦 are the catenoid, the helicoid and three 1-parameter families of surfaces: the simply and doubly periodic Scherk minimal surfaces and the Riemann minimal examples.


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Joaquín Pérez. M. Magdalena Rodríguez. Martin Traizet. "The classification of doubly periodic minimal tori with parallel ends." J. Differential Geom. 69 (3) 523 - 577, Mar 2005.


Published: Mar 2005
First available in Project Euclid: 27 July 2005

zbMATH: 1094.53007
MathSciNet: MR2170278
Digital Object Identifier: 10.4310/jdg/1122493998

Rights: Copyright © 2005 Lehigh University

Vol.69 • No. 3 • Mar 2005
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