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arXiv · 2203.05448

Symplectic non-convexity of toric domains

Julien Dardennes·Jean Gutt·Jun Zhang
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Abstract

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.

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Julien Dardennes, Jean Gutt, Jun Zhang. 2022-03-10. Symplectic non-convexity of toric domains. https://arxiv.org/abs/2203.05448

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