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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2024 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2024
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212783 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| Summary: | 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.
|
|---|---|
| ISSN: | 1815-0659 |