Skip to content
DraconiticResearch
Search Sources API
181,716 studies31 sourcesUpdated 58 min ago
PreprintarXiv licencearXiv

The ECH and alternative ECH capacities of closed symplectic 4-manifolds

  • Gabriel Beiner
Open at sourcePDFDOICite

Abstract

We show that the ECH capacities of every closed symplectic 4-manifold are infinite. We also give the first examples of symplectic 4-manifolds whose alternative ECH capacities are infinite. We verify the ECH Weyl law holds with bounded subleading asymptotics for the alternative ECH capacities of any closed symplectic 4-manifold with b2+=1 or any smooth domain therewithin.

Related

  1. Symplectic capacities and Weyl laws from Abelian Higgs min max theory
    Taisuke Shibata
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  2. Fedosov manifolds with parallel symplectic Weyl curvature
    Shane Rankin, Ivo Terek
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  3. Symplectic four-manifolds and hyperbolic π-orbifolds
    Francesco Lin, Bruno Martelli
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  4. Finite Symplectic Automorphisms of Hyperkähler Manifolds of K3[n]-Type Act Trivially on Discriminant Groups
    Jie Fu, Shihao Wang, Zhiwei Zheng
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Mazur manifolds and symplectic structures
    Alberto Cavallo
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{beiner2026alternative,
  title = {{The ECH and alternative ECH capacities of closed symplectic 4-manifolds}},
  author = {Gabriel Beiner},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.19042},
  eprint = {2608.19042},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.19042},
}
RIS
TY  - UNPB
TI  - The ECH and alternative ECH capacities of closed symplectic 4-manifolds
AU  - Gabriel Beiner
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2608.19042
UR  - https://arxiv.org/abs/2608.19042
AB  - We show that the ECH capacities of every closed symplectic 4-manifold are infinite. We also give the first examples of symplectic 4-manifolds whose alternative ECH capacities are infinite. We verify the ECH Weyl law holds with bounded subleading asymptotics for the alternative ECH capacities of any closed symplectic 4-manifold with b_2^+=1 or any smooth domain therewithin.
ER  -