Regarding a uniqueness property of singly-periodic Scherk surfaces

Jacob Bernstein

Regarding a uniqueness property of singly-periodic Scherk surfaces

Differential Geometry 2013-05-14 v2

Authors: Jacob Bernstein

Abstract

Inspired by an argument of Ros [15] -- we use the L\'{o}pez-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.

Keywords

Scherk surfaces minimal surfaces uniqueness property López-Ros deformation singly-periodic area growth

Cite

@article{arxiv.1303.4221,
  title  = {Regarding a uniqueness property of singly-periodic Scherk surfaces},
  author = {Jacob Bernstein},
  journal= {arXiv preprint arXiv:1303.4221},
  year   = {2013}
}

Comments

This paper has been withdrawn by the author due to the incorrect and overly strong statement of Proposition B.3.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

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