Robustly non-convex hypersurfaces in contact manifolds
Abstract
We construct the first examples of hypersurfaces in any contact manifold of dimension 5 and larger that cannot be C2-approximated by convex hypersurfaces, contrasting sharply with the foundational results of Giroux in dimension 3 and Honda-Huang in the C0 case. The main technical step is the first construction of a dynamical blender in the contact setting.
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