PreprintCC BY 4.0arXiv
Counting Minimal Lagrangians Via Mirzakhani Functions
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 A6(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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BibTeX
@misc{lowe2026counting,
title = {{Counting Minimal Lagrangians Via Mirzakhani Functions}},
author = {Ben Lowe and Fernando C. Marques and André Neves},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.04614},
eprint = {2605.04614},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.04614},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Counting Minimal Lagrangians Via Mirzakhani Functions
AU - Ben Lowe
AU - Fernando C. Marques
AU - André Neves
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2605.04614
UR - https://arxiv.org/abs/2605.04614
AB - 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.
ER -