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Creators/Authors contains: "Ramos, Vinicius_G_B"

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  1. ; (, Revista Matemática Iberoamericana)
    It is a long-standing conjecture that all symplectic capacities which are equal to the Gromov width for ellipsoids coincide on a class of convex domains in\mathbb{R}^{2n}. It is known that they coincide for monotone toric domains in all dimensions. In this paper, we study whether requiring a capacity to be equal to thekth Ekeland–Hofer capacity for all ellipsoids can characterize it on a class of domains. We prove that fork=n=2, this holds for convex toric domains, but not for all monotone toric domains. We also prove that, fork=n\ge 3, this does not hold even for convex toric domains. 
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    Free, publicly-accessible full text available July 8, 2026
  2. ; ; ; (, International Mathematics Research Notices)
    Abstract Chaidez and Edtmair have recently found the first examples of dynamically convex domains in $$\mathbb{R}^{4}$$ that are not symplectomorphic to convex domains, answering a long-standing open question. In this paper, we discover new examples of such domains without referring to Chaidez–Edtmair’s methods. We show a stronger result: that these domains are arbitrarily far from the set of convex domains in $$\mathbb{R}^{4}$$ with respect to the coarse symplectic Banach–Mazur distance. 
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  3. ; ; (, Compositio Mathematica)
    Abstract In this paper we use the periodic Toda lattice to show that certain Lagrangian product configurations in the classical phase space are symplectically equivalent to toric domains. In particular, we prove that the Lagrangian product of a certain simplex and the Voronoi cell of the root lattice$$A_n$$is symplectically equivalent to a Euclidean ball. As a consequence, we deduce that the Lagrangian product of an equilateral triangle and a regular hexagon is symplectomorphic to a Euclidean ball in dimension 4. 
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    Free, publicly-accessible full text available February 1, 2026