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arXiv · 2206.07847

Disk-like surfaces of section and symplectic capacities

Oliver Edtmair
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Abstract

We prove that the cylindrical capacity of a dynamically convex domain in $\mathbb{R}^4$ agrees with the least symplectic area of a disk-like global surface of section of the Reeb flow on the boundary of the domain. Moreover, we prove the strong Viterbo conjecture for all convex domains in $\mathbb{R}^4$ which are sufficiently $C^3$ close to the round ball. This generalizes a result of Abbondandolo-Bramham-Hryniewicz-Salom\~{a}o establishing a systolic inequality for such domains.

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Oliver Edtmair. 2022-06-15. Disk-like surfaces of section and symplectic capacities. https://arxiv.org/abs/2206.07847

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