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Higher genus Riemann minimal surfaces

Laurent Hauswirth·Frank Pacard
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Abstract

We construct higher genus Riemann's minimal surfaces properly embedded in the Euclidean space. To do that we glue end by end a Costa-Hoffman-Meeks examples to two halves genus zero Riemann's minimal surfaces. In first we need to perform a deformation of a Costa-Hoffman-Meeks example to prescribe the flux vector along the catenoidal ends. Then we study the mapping property of the Jacobi operator on the half Riemann example as a perturbation analysis of a CMC-Delaunay half cylinder.

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Laurent Hauswirth, Frank Pacard. 2005-11-17. Higher genus Riemann minimal surfaces. https://arxiv.org/abs/math/0511438

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