arXiv subjects

Julien Dardennes

Publications and source records attributed to Julien Dardennes.

2 recordsLinked to original sources

arXiv2023

Coarse distance from dynamically convex to convex

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.

math.SG↗

arXiv2022

Symplectic non-convexity of toric domains

We investigate the convexity up to symplectomorphism (called symplectic convexity) of star-shaped toric domains in $\mathbb R^4$. In particular, based on the criterion from Chaidez-Edtmair via Ruelle invariant and systolic ratio of the boundary of star-shaped toric domains, we provide elementary operations on domains that can kill the symplectic convexity. These operations only result in $C^0$-small perturbations in terms of domains' volume. Moreover, one of the operations is a systematic way to produce examples of dynamically convex but not symplectically convex toric domains. Finally, we are able to provide concrete bounds for the constants that appear in Chaidez-Edtmair's criterion.

math.SG↗