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Bibliographic Details
Main Authors: Lowe, Ben, Marques, Fernando C., Neves, André
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.04614
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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