Matthew Badger

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math.MG2026

Space-filling surfaces: sharp Hölder continuous parameterizations from squares to cubes

Matthew Badger, Kevin Palmer

Following a hint of Semmes, we employ Stong's bijections between integer lattices to construct space-filling surfaces, which are higher-dimensional analogues of space-filling curve…

math.MG2026

Tangents to Lipschitz and Sobolev images

Matthew Badger, Jared Krandel, Vyron Vellis

We develop geometric versions of Rademacher and Calderon type differentiability theorems in two categories. A special case of our results is that for any Lipschitz or continuous $W…

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…