English

Robustly non-convex hypersurfaces in contact manifolds

Symplectic Geometry 2025-09-30 v3 Dynamical Systems

Abstract

We construct the first examples of hypersurfaces in any contact manifold of dimension 5 and larger that cannot be C2C^2-approximated by convex hypersurfaces, contrasting sharply with the foundational results of Giroux in dimension 33 and Honda-Huang in the C0C^0 case. The main technical step is the first construction of a dynamical blender in the contact setting.

Keywords

Cite

@article{arxiv.2406.05979,
  title  = {Robustly non-convex hypersurfaces in contact manifolds},
  author = {Julian Chaidez},
  journal= {arXiv preprint arXiv:2406.05979},
  year   = {2025}
}

Comments

39 pages + references. 3 figures. v3 has a rewritten introduction, minor corrections and improved exposition