类盘曲面的剖面和交映容积

IF 2.4 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis Pub Date : 2024-07-16 DOI:10.1007/s00039-024-00689-4

O. Edtmair

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引用次数: 0

摘要

我们证明了在\({\mathbb{R}}^{4}\)中的动态凸域的圆柱容量与该域边界上的里布流的圆盘状全局截面的最小交映面积一致。此外，我们证明了在\({\mathbb{R}}^{4}\)中所有足够 C3 接近圆球的凸域的强维特博猜想。这概括了 Abbondandolo-Bramham-Hryniewicz-Salomão 的一个结果，即为此类域建立了一个收缩不等式。

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Disk-Like Surfaces of Section and Symplectic Capacities

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 C³ close to the round ball. This generalizes a result of Abbondandolo-Bramham-Hryniewicz-Salomão establishing a systolic inequality for such domains.

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来源期刊

Geometric and Functional Analysis 数学-数学

CiteScore

3.70

自引率

4.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.