In the first paper, we prove that for a closed Legendrian submanifold L of dimension n>2 with a loose chart of size η, any Legendrian isotopy starting at L can be C0-approximated by a Legendrian isotopy with energy arbitrarily close to η/2. This in particular implies that the displacement energy of loose displaceable Legendrians is bounded by half the size of its smallest loose chart, which proves a conjecture of Dimitroglou Rizell and Sullivan. In the second paper, we show that the Legendrian lift of an exact, displaceable Lagrangian has vanishing Shelukhin-Chekanov-Hofer pseudo-metric by lifting an argument due to Sikorav to the contactization. In particular, this proves the existence of such Legendrians, providing counterexamples to a conjecture of Rosen and Zhang. After completion of the manuscript, we noticed that Cant (arXiv:2301.06205) independently proved a more general version of our main result.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-502058 |
| Date | January 2023 |
| Creators | Nakamura, Lukas |
| Publisher | Uppsala universitet, Matematiska institutionen, Uppsala |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Licentiate thesis, comprehensive summary, info:eu-repo/semantics/masterThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | U.U.D.M. report / Uppsala University, Department of Mathematics, 1101-3591 ; 2023:2 |
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