Regarding a uniqueness property of singly-periodic Scherk surfaces

Abstract

Inspired by an argument of Ros [15] -- we use the López-Ros deformation to give another proof of the fact -- due to Meeks and Wolf [13] -- that the only smooth, connected, singly-periodic minimal surfaces in $\Real^3$ with the area growth of two planes are the singly-periodic Scherk surfaces.

This paper has been withdrawn by the author due to the incorrect and overly strong statement of Proposition B.3. This leads to a serious gap in the proof of Proposition 3.5