, Volume 62, Issue 1, pp 83-114

Embedded minimal surfaces derived from Scherk's examples

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In this article we construct embedded minimal surfaces which are, at least heuristically, derived from Scherk's first and second surface. Our examples are either parametrized by punctured spheres and then have one translational period or one screw motion period; or they are parametrized by rectangular tori and then have one or two translational periods. The helicoidal examples contain nonisometric ∈-deformations in the sense of Rosenberg [R].