Planar sets with large visible parts

Tuomas Orponen

Planar sets with large visible parts

Classical Analysis and ODEs 2026-06-29 v1 Metric Geometry

Authors: Tuomas Orponen

Abstract

I construct a compact subset of the plane whose visible parts are $\tfrac{3}{2}$ -dimensional in all directions. This disproves the visibility conjecture. The value $\tfrac{3}{2}$ cannot be increased, as shown in recent collaboration with A. Rutar.

Cite

@article{arxiv.2606.29839,
  title  = {Planar sets with large visible parts},
  author = {Tuomas Orponen},
  journal= {arXiv preprint arXiv:2606.29839},
  year   = {2026}
}

Comments

20 pages