On the Lagrangian capacity of convex or concave toric domains
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910602737221632 |
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| author | Pereira, Miguel |
| author_facet | Pereira, Miguel |
| contents | We establish computational results concerning the Lagrangian capacity, originally defined by Cieliebak-Mohnke. More precisely, we show that the Lagrangian capacity of a 4-dimensional convex toric domain is equal to its diagonal. Working under the assumption that there is a suitable virtual perturbation scheme which defines the curve counts of linearized contact homology, we extend the previous result to any convex or concave toric domain. This result gives a positive answer to a conjecture of Cieliebak-Mohnke for the Lagrangian capacity of the ellipsoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_11022 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Lagrangian capacity of convex or concave toric domains Pereira, Miguel Symplectic Geometry We establish computational results concerning the Lagrangian capacity, originally defined by Cieliebak-Mohnke. More precisely, we show that the Lagrangian capacity of a 4-dimensional convex toric domain is equal to its diagonal. Working under the assumption that there is a suitable virtual perturbation scheme which defines the curve counts of linearized contact homology, we extend the previous result to any convex or concave toric domain. This result gives a positive answer to a conjecture of Cieliebak-Mohnke for the Lagrangian capacity of the ellipsoid. |
| title | On the Lagrangian capacity of convex or concave toric domains |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2207.11022 |