# Lower bounds for codimension-1 measure in metric manifolds

@article{Kinneberg2018LowerBF, title={Lower bounds for codimension-1 measure in metric manifolds}, author={Kyle Kinneberg}, journal={Revista Matem{\'a}tica Iberoamericana}, year={2018} }

We establish Euclidean-type lower bounds for the codimension-1 Hausdorff measure of sets that separate points in doubling and linearly locally contractible metric manifolds. This gives a quantitative topological isoperimetric inequality in the setting of metric manifolds, in the sense that lower bounds for the codimension-1 measure of a set depend not on some notion of filling or volume but rather on in-radii of complementary components. As a consequence, we show that balls in a closed…

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