Lagrangian Surplusection Phenomena
Suppose you have a family of Lagrangian submanifolds ₜ and an auxiliary Lagrangian . Suppose that intersects some of the ₜ more than the minimal number of times. Can you eliminate surplus intersection (surplusection) with all fibres by performing a Hamiltonian isotopy of ? Or will any Lagrangian is...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| ISSN: | 1815-0659 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212783 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Lagrangian Surplusection Phenomena. Georgios Dimitroglou Rizell and Jonathan David Evans. SIGMA 20 (2024), 109, 13 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Suppose you have a family of Lagrangian submanifolds ₜ and an auxiliary Lagrangian . Suppose that intersects some of the ₜ more than the minimal number of times. Can you eliminate surplus intersection (surplusection) with all fibres by performing a Hamiltonian isotopy of ? Or will any Lagrangian isotopic to surplusect some of the fibres? We argue that in several important situations, surplusection cannot be eliminated, and that a better understanding of surplusection phenomena (better bounds and a clearer understanding of how the surplusection is distributed in the family) would help to tackle some outstanding problems in different areas, including Oh's conjecture on the volume-minimising property of the Clifford torus and the concurrent normals conjecture in convex geometry. We pose many open questions.
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| ISSN: | 1815-0659 |