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arXiv · 2406.05979

Robustly non-convex hypersurfaces in contact manifolds

Julian Chaidez
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Abstract

We construct the first examples of hypersurfaces in any contact manifold of dimension 5 and larger that cannot be $C^2$-approximated by convex hypersurfaces, contrasting sharply with the foundational results of Giroux in dimension $3$ and Honda-Huang in the $C^0$ case. The main technical step is the first construction of a dynamical blender in the contact setting.

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Julian Chaidez. 2024-06-10. Robustly non-convex hypersurfaces in contact manifolds. https://arxiv.org/abs/2406.05979

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