Abstract
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.
Citation
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. https://doi.org/10.4310/jdg/1122493998
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