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Results tagged with hausdorff-measure
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user 1441
Questions about Hausdorff measures, their variants (such as spherical Hausdorff measures) and generalisations.
1
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Recovering the length metric from Hausdorff measure
Nan Li proved that it holds for a pair of Alexandrov spaces without boundary;
in particular, it solves the problem for Riemannian manifolds.
See Lipschitz-Volume rigidity in Alexandrov geometry.
It se …
- 45k
20
votes
Accepted
Hausdorff measure and the volume form
I guess you know that it is true in $\mathbb R^k$.
Without loss of generality we can assume that $f\geqslant 0$.
Fix $\varepsilon>0$ and cover your manifold by $(1\mp\varepsilon)$-Lipschitz charts.
Br …
- 45k