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arXiv · 2308.06604

Coarse distance from dynamically convex to convex

Julien Dardennes·Jean Gutt·Vinicius G. B. Ramos·Jun Zhang
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Abstract

Chaidez and Edtmair have recently found the first example of dynamically convex domains in $\mathbb R^4$ that are not symplectomorphic to convex domains (called symplectically convex domains), answering a long-standing open question. In this paper, we discover new examples of such domains without referring to Chaidez-Edtmair's criterion. We also show that these domains are arbitrarily far from the set of symplectically convex domains in $\mathbb R^4$ with respect to the coarse symplectic Banach-Mazur distance by using an explicit numerical criterion for symplectic non-convexity.

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Julien Dardennes, Jean Gutt, Vinicius G. B. Ramos, Jun Zhang. 2023-08-12. Coarse distance from dynamically convex to convex. https://arxiv.org/abs/2308.06604

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