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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.04614 |
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| _version_ | 1866913098385850368 |
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| author | Lowe, Ben Marques, Fernando C. Neves, André |
| author_facet | Lowe, Ben Marques, Fernando C. Neves, André |
| contents | We show that for $k>1$ the number of genus $k$ minimal Lagrangians with area at most $A$ in a product of hyperbolic surfaces grows on the order of $A^{6(k-1)}$, with an explicit leading constant given in terms of the Mirzakhani function. We also prove rigidity of the Lagrangian area spectrum, and obtain analogous counting results for products of a higher genus surface with a circle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04614 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Counting Minimal Lagrangians Via Mirzakhani Functions Lowe, Ben Marques, Fernando C. Neves, André Differential Geometry Dynamical Systems Geometric Topology We show that for $k>1$ the number of genus $k$ minimal Lagrangians with area at most $A$ in a product of hyperbolic surfaces grows on the order of $A^{6(k-1)}$, with an explicit leading constant given in terms of the Mirzakhani function. We also prove rigidity of the Lagrangian area spectrum, and obtain analogous counting results for products of a higher genus surface with a circle. |
| title | Counting Minimal Lagrangians Via Mirzakhani Functions |
| topic | Differential Geometry Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2605.04614 |