A rigidity theorem for Riemann's minimal surfaces
Romon, Pascal
HAL, hal-00862672 / Harvested from HAL
Text on HAL
We describe first the analytic structure of Riemann's examples of singly-periodic minimal surfaces; we also characterize them as extensions of minimal annuli bounded by parallel straight lines between parallel planes. We then prove their uniqueness as solutions of the perturbed problem of a punctured annulus, and we present standard methods for determining finite total curvature periodic minimal surfaces and solving the period problems.
Publié le : 1993-07-05
Classification:  complete minimal surface,  singly periodic,  embeddedness,  period problem,  MSC 53A10, 53C42,  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] 
@article{hal-00862672,
     author = {Romon, Pascal},
     title = {A rigidity theorem for Riemann's minimal surfaces},
     journal = {HAL},
     volume = {1993},
     number = {0},
     year = {1993},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00862672}
}

Romon, Pascal. A rigidity theorem for Riemann's minimal surfaces. HAL, Tome 1993 (1993) no. 0, . http://gdmltest.u-ga.fr/item/hal-00862672/