Guy Lachman

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math.SP2026

Determinants of Laplacians on converging hyperbolic surfaces

Renan Gross, Guy Lachman, Asaf Nachmias

Let $S_{k}$ be a sequence of compact hyperbolic surfaces of increasing volume which locally converges to a random rooted surface. We show that if the normalized sum of the reciprocal…

math.SP2025

A sharp lower bound on the small eigenvalues of surfaces

Renan Gross, Guy Lachman, Asaf Nachmias

Let $S$ be a compact hyperbolic surface of genus $g \geq 2$ and let $I (S) = \frac{1}{Vol ( S )} \int_{S} \frac{1}{Inj ( x ) ^{2} \land 1} d x$ , where $Inj (x)$ is th…