Pré-Publication, Document De Travail Année : 2025

COARSE DISTANCE FROM DYNAMICALLY CONVEX TO CONVEX

Résumé

Chaidez and Edtmair have recently found the first examples of dynamically convex domains in 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 in [3]. We also show that these domains are arbitrarily far from the set of symplectically convex domains in R 4 with respect to the coarse symplectic Banach-Mazur distance by using an explicit numerical criterion for symplectic non-convexity.

Along with the proof of Theorem 1.1, we discover a family of dynamically convex domains X Ωp (see (3)), parametrized by p ∈ (0, 1], that are not symplectomorphic to convex ones when p is sufficiently small.

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Dates et versions

hal-04920068 , version 1 (29-01-2025)

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  • HAL Id : hal-04920068 , version 1

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Julien Dardennes, Jean Gutt, Vinicius Ramos, Jun Zhang. COARSE DISTANCE FROM DYNAMICALLY CONVEX TO CONVEX. 2025. ⟨hal-04920068⟩
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