A parabolic minimal surface in R3 intersects every nonflat properly embedded minimal surface of bounded curvature

Franc Forstneric

A parabolic minimal surface in R3 intersects every nonflat properly embedded minimal surface of bounded curvature

Differential Geometry 2022-07-06 v2

Authors: Franc Forstneric

Abstract

We show that the image of a nonconstant conformal harmonic map $\mathbb C\to \mathbb R^3$ , not necessarily proper and possibly with branch points, intersects every properly embedded nonflat minimal surface of bounded curvature in $\mathbb R^3$ . The same holds if $\mathbb C$ is replaced by any open conformal surface without nonconstant bounded subharmonic functions.

Keywords

minimal surface conformal harmonic map bounded curvature properly embedded subharmonic function

Cite

@article{arxiv.2206.06045,
  title  = {A parabolic minimal surface in R3 intersects every nonflat properly embedded minimal surface of bounded curvature},
  author = {Franc Forstneric},
  journal= {arXiv preprint arXiv:2206.06045},
  year   = {2022}
}

Comments

The paper is withdrawn due to significant overlap with preexisting papers

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