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Title: Strangling of the fundamental gap in hyperbolic space.

Abstract: For the Laplace operator with Dirichlet boundary conditions on convex domains in $H^n, n ≥ 2$, we prove that the product of the fundamental gap with the square of the diameter can be arbitrarily small for domains of any diameter. This property distinguishes hyperbolic spaces from Euclidean and spherical ones, where the quantity is bounded below by $3 \pi^2$.

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