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arXiv · 2605.04614

Counting Minimal Lagrangians Via Mirzakhani Functions

Ben Lowe·Fernando C. Marques·André Neves
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Abstract

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, and we obtain a similar result for products of nonpositively curved surfaces. We also prove rigidity of the Lagrangian area spectrum, and obtain analogous counting results for products of a higher genus surface with a circle.

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Ben Lowe, Fernando C. Marques, André Neves. 2026-05-06. Counting Minimal Lagrangians Via Mirzakhani Functions. https://arxiv.org/abs/2605.04614

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