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Bibliographic Details
Main Authors:	Lowe, Ben, Marques, Fernando C., Neves, André
Format:	Preprint
Published:	2026
Subjects:	Differential Geometry Dynamical Systems Geometric Topology
Online Access:	https://arxiv.org/abs/2605.04614
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Table of 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.