Properness of minimal surfaces with bounded curvature

G. Pacelli Bessa; Luquesio P. Jorge

Properness of minimal surfaces with bounded curvature

Differential Geometry 2007-05-23 v1 Metric Geometry

Authors: G. Pacelli Bessa , Luquesio P. Jorge

Abstract

We show that immersed minimal surfaces of $\mathbb{R}^{3}$ with bounded curvature and proper self intersections are proper. We also show that the restriction of the immersing map to a wide component is always proper. When the immersing map is injective the whole surface is a wide component. Prior to these results it was only known that injectively immersed minimal surfaces with bounded curvature were proper.

Keywords

minimal surfaces bounded curvature proper immersions self intersections wide component immersing map

Cite

@article{arxiv.math/0205304,
  title  = {Properness of minimal surfaces with bounded curvature},
  author = {G. Pacelli Bessa and Luquesio P. Jorge},
  journal= {arXiv preprint arXiv:math/0205304},
  year   = {2007}
}

Comments

Short paper, (4 pages), writen in ams-latex

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