Minimal surfaces in $R^3$ with dihedral symmetry

Details Minimal surfaces in $R^3$ with dihedral symmetry Minimal surfaces in $R^3$ with dihedral symmetry

2008-04-26

arxiv.org/abs/0804.4205v1

Tohoku Math J. 47 (1995), 31-54

Mathematics

Differential Geometry

Scientific paper

We construct new examples of immersed minimal surfaces with catenoid ends and finite total curvature, of both genus zero and higher genus. In the genus zero case, we classify all such surfaces with at most $2n+1$ ends, and with symmetry group the natural $\bfZ_2$ extension of the dihedral group $D_n$. The surfaces are constructed by proving existence of the conjugate surfaces. We extend this method to cases where the conjugate surface of the fundamental piece is noncompact and is not a graph over a convex plane domain.

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