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arXiv · 1602.06440

Lower bounds for codimension-1 measure in metric manifolds

Kyle Kinneberg
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Abstract

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, connected, doubling, and linearly locally contractible metric $n$-manifold $(M,d)$ with radius $0 0$ depends only on $n$ and on the doubling and linear local contractibility constants.

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Kyle Kinneberg. 2016-02-20. Lower bounds for codimension-1 measure in metric manifolds. https://arxiv.org/abs/1602.06440

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