# Minimal surfaces in \$R^3\$ with dihedral symmetry - Mathematics > Differential Geometry

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Abstract: We construct new examples of immersed minimal surfaces with catenoid ends andfinite total curvature, of both genus zero and higher genus. In the genus zerocase, we classify all such surfaces with at most \$2n+1\$ ends, and with symmetrygroup the natural \$\bfZ 2\$ extension of the dihedral group \$D n\$. The surfacesare constructed by proving existence of the conjugate surfaces. We extend thismethod to cases where the conjugate surface of the fundamental piece isnoncompact and is not a graph over a convex plane domain.

Autor: Wayne Rossman

Fuente: https://arxiv.org/