Properness of minimal surfaces with bounded curvature

Details Properness of minimal surfaces with bounded curvature Properness of minimal surfaces with bounded curvature

2002-05-28

arxiv.org/abs/math/0205304v1

An. Acad. Bras. Cienc., Sept 2003, vol.75, no.3, p.279-284.

Mathematics

Differential Geometry

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

Scientific paper

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.

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