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math.MG2026
On solid angles and simplex shape measures
Martin W. Licht
The minimum solid angle of a simplex is shown to be a shape measure in any dimension. While this has been known in dimensions two and three, the higher-dimensional generalization i…
math.MG2023
On Lipschitz partitions of unity and the Assouad--Nagata dimension
Martin W. Licht
We show that the standard partition of unity subordinate to an open cover of a metric space has Lipschitz constant , where is the Lebesgue nu…