, Volume 133, Issue 1, pp 107-132

Uniqueness of the Riemann minimal examples

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We prove that a properly embedded minimal surface in R 3 of genus zero with infinite symmetry group is a plane, a catenoid, a helicoid or a Riemann minimal example. We introduce the language of Hurwitz schemes to understand the underlying moduli space of surfaces in our setting.

Oblatum 30-V-1997 & 5-VIII-1997