Disk-like surfaces of section and symplectic capacities
Reviewed by Pithpith:44FWK3HVopen to challenge →
read the original 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.
This paper has not been read by Pith yet.
Forward citations
Cited by 1 Pith paper
-
Symplectic capacities of $S^1$-invariant dynamically convex domains in $\mathbb{R}^4$
All normalized symplectic capacities agree on S^1-invariant dynamically convex domains in R^4, with necessary and sufficient conditions for dynamic convexity under the given invariance.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.