The number of genus-k minimal Lagrangians of area ≤ A in a product of hyperbolic surfaces grows asymptotically as c A^{6(k-1)} where c is an explicit constant given in terms of the Mirzakhani function.
Catanese,Fibred surfaces, varieties isogenous to a product and related moduli spaces, Amer
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Counting Minimal Lagrangians Via Mirzakhani Functions
The number of genus-k minimal Lagrangians of area ≤ A in a product of hyperbolic surfaces grows asymptotically as c A^{6(k-1)} where c is an explicit constant given in terms of the Mirzakhani function.