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arXiv · 2607.03649

Convex hypersurfaces and robust heterodimensional dynamics

Julian Chaidez·Michael Huang
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Abstract

We prove that any closed orientable hypersurface in a contact manifold of dimension five or greater is isotopic to a robustly non-convex hypersurface via an arbitrarily $C^0$-small isotopy. This strengthens a recent result of the first author and yields a strong counterpart to the groundbreaking density theorem of Honda-Huang and Giroux. This is proven by combining a new convexity obstruction via heteroclinics and recent advances in robust heterodimensional dynamics due to Li-Turaev to produce a robust deconvexifying plug, which is a local and robust convexity obstruction.

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Julian Chaidez, Michael Huang. 2026-07-04. Convex hypersurfaces and robust heterodimensional dynamics. https://arxiv.org/abs/2607.03649

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