Establishes equivalence between vanishing of bounded fundamental class and positivity of Cheeger constant for negatively curved infinite-volume manifolds with bounded geometry, solving one direction of Kim-Kim conjecture in full generality.
Aperiodic tilings, positive scalar curvature, and amenability of spaces.Journal of the American Mathematical Society, 5(4):907–918
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Bounded volume class and Cheeger isoperimetric constant for negatively curved manifolds
Establishes equivalence between vanishing of bounded fundamental class and positivity of Cheeger constant for negatively curved infinite-volume manifolds with bounded geometry, solving one direction of Kim-Kim conjecture in full generality.