### Citations

62 |
Embedded minimal surfaces derived from Scherk’s examples
- Karcher
- 1988
(Show Context)
Citation Context ... with four parallel ends in quotients of R 3 by two independent translations, which we will call the standard examples. These surfaces generalize the examples given by Karcher, Meeks and Rosenberg in =-=[3, 4, 7]-=-. K can be endowed with a natural structure of a self-conjugated 3-dimensional real analytic manifold diffeomorphic to R × ( R 2 − {(±1, 0)} ) whose degenerate limits are the catenoid, the helicoid, t... |

48 | Construction of minimal surfaces. Surveys in Geometry, University of Tokyo 1–96 - Karcher - 1989 |

41 | Schrödinger operators associated to a holomorphic map
- Montiel, Ros
- 1990
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Citation Context ... avoid repeating surfaces twice, see Remark 2. Remark 3 By construction, the branch values of the Gauss map N of Mθ,α,β are contained in a spherical equator of S 2 , so a consequence of Theorem 14 in =-=[8]-=- assures that the space of bounded Jacobi functions on M coincides with the space of linear functions of N, {〈N, V 〉 | V ∈ R 3 } (in particular, such space is 3-dimensional). This condition is usually... |

35 | Bemerkungen über die kleinste Fläche innerhalb gegebener - Scherk |

34 |
H.: The global theory of doubly periodic minimal surfaces
- Meeks, Rosenberg
- 1989
(Show Context)
Citation Context ... with four parallel ends in quotients of R 3 by two independent translations, which we will call the standard examples. These surfaces generalize the examples given by Karcher, Meeks and Rosenberg in =-=[3, 4, 7]-=-. K can be endowed with a natural structure of a self-conjugated 3-dimensional real analytic manifold diffeomorphic to R × ( R 2 − {(±1, 0)} ) whose degenerate limits are the catenoid, the helicoid, t... |

19 | The classification of doubly periodic minimal tori with parallel ends
- Pérez, Rodríguez, et al.
(Show Context)
Citation Context ...o R × ( R 2 − {(±1, 0)} ) whose degenerate limits are the catenoid, the helicoid, the simply and doubly periodic Scherk minimal surfaces and the Riemann minimal examples. Pérez, Rodríguez and Traizet =-=[9]-=- characterize K in the following sense: If M is a properly embedded minimal torus in a quotient of R 3 by two independent translations with any number of parallel ends, then M is a finite covering of ... |

18 |
Uniqueness of the Riemann minimal examples
- Pérez, Ros
- 1998
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Citation Context ..., is diffeomorphic to R × (R 2 − {(±1, 0)}). The proof of Theorem 3 is inspired by the arguments of Pérez, Traizet and the author [9] to prove Theorem 2 (they follow the ideas of Meeks, Pérez and Ros =-=[6]-=-). We model the family K of standard examples as an analytic subset in a complex manifold W of finite dimension (roughly, W consists of all admissible Weierstrass data for our problem). In the boundar... |

6 |
The space of embedded doubly-periodic minimal surfaces
- Hauswirth, Traizet
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Citation Context ...literature as the nondegeneracy of Mθ,α,β, which can be interpreted by means of an Implicit Function Theorem argument to obtain that K is a 3-dimensional real analytic manifold (Hauswirth and Traizet =-=[1]-=-). 2.3 The space of standard examples is self-conjugate In the previous subsection we have defined the family K = {Mθ,α,β | (θ, α, β) ∈ I} of standard examples. Given Mθ,α,β ∈ K with Weierstrass data ... |

2 |
Meeks III. Classification des surfaces minimales de genre zéro proprement plongées dans R
- Lazard-Holly, H
- 1997
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Citation Context .... ∗ Research partially supported by a MEC/FEDER grant no. MTM2004-02746. 1 Unless explicitly mentioned, all surfaces in the paper are supposed to be connected and orientable. 1Lazard-Holly and Meeks =-=[5]-=- proved that these are the only possible examples in this setting; i.e., if the quotient of a doubly periodic minimal surface M ⊂ R 3 has genus zero, then M must be a doubly periodic Scherk minimal su... |