Higher genus Riemann minimal surfaces

Details Higher genus Riemann minimal surfaces Higher genus Riemann minimal surfaces

2005-11-17

arxiv.org/abs/math/0511438v1

Mathematics

Differential Geometry

43 pages

Scientific paper

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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