Convex hypersurfaces and robust heterodimensional dynamics

2026/07/04 by Julian Chaidez, Michael Huang · 1 voice
Mathematics · #math.SG #math.DS

paper · pdf

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 C⁰-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.

Citations

• Conformally symplectic topology from a dynamical viewpoint
• Robust heterodimensional cycles of co-index two via split blending machines
• Robustly non-convex hypersurfaces in contact manifolds
• The Giroux correspondence in arbitrary dimensions
• Morse-Smale characteristic foliations and convexity in contact manifolds
• Convex hypersurface theory in contact topology
• Bypass attachments in higher-dimensional contact topology
• What is ... a blender?
• Partial hyperbolicity and classification: a survey
• Symbolic blender-horseshoes and applications
• Right-veering diffeomorphisms of compact surfaces with boundary I
• Right-veering diffeomorphisms of compact surfaces with boundary II
• Cabling and transverse simplicity
• Convex decomposition theory
• Tight contact structures with no symplectic fillings
• On the classification of tight contact structures I
• On the non-existence of tight contact structures

Discussions

• Julian Chaidez, Michael Huang: Convex hypersurfaces and robust heterodimensional dynamics https://arxiv.org/abs/2607.03649 https://arxiv.org/pdf/2607.03649 https://arxiv.org/html/2607.03649 [bsky, 0 points, 0 comments]

Related

• Robustly non-convex hypersurfaces in contact manifolds
• Honda-Huang's work on contact convexity revisited
• Convex hypersurface theory in contact topology
• A proof of the classification theorem of overtwisted contact structures via convex surface theory
• Convex decomposition theory