Raanan Schul

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20242026

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math.MG2025

Characterizing rectifiability via biLipschitz pieces of Lipschitz mappings on the space

Sean Li, Raanan Schul

We give the following characterization of rectifiable metric spaces. A metric space with positive lower Hausdorff density is rectifiable if and only if, for any subset $F$ and $f:F…

math.MG2025

Square packings and rectifiable doubling measures

Matthew Badger, Raanan Schul

We prove that for all integers $2 \leq m \leq d - 1$ , there exists doubling measures on $R^{d}$ with full support that are $m$ -rectifiable and purely $(m - 1)$ -unrectifiable in th…