Convex hypersurfaces and robust heterodimensional dynamics

Julian Chaidez, Michael Huang

arXiv:2607.03649v1 Primary: math.SG Secondary: math.DS

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.

Disclosure

“surfaces in contact manifolds). In Sections 3 and 4, we prove Theorems 10 and 14 respectively. In Section 5, we provide key background on non-degeneracy and unfoldings from [38]. Finally, in Section 6 we prove Theorem 15. Acknowledgements. AI tools were used solely for proofreading this manuscript. JC and MH were partially supported by NSF Award DMS-2446019 and US-Israel BSF Award 2024157.”
PDF page 6

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Structural counts

Pages 47 pdf

Theorems 8 source

Lemmas 32 source

Propositions 6 source

Corollaries 5 source

Definitions 41 source

Displayed equations 336 source

Bibliography entries 172 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file main.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.