Caleb Marshall

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20242026

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math.CA2026

Nearly Sharp Uniform Projection Bounds and Superlinear Vitushkin Inequalities for Deterministic Self-Similar Sets

Caleb Marshall

For each $α \in (0, 1)$ , we construct an explicit deterministic finite homogeneous planar iterated function system of similarities satisfying the strong separation condition, whose at…

math.CA2026

Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint

Caleb Marshall

For a $1$ -rectifiable set $E \subset R^{d}$ of positive length, a theorem of Federer shows that, among any $d$ linearly independent orthogonal projections of $E$ , at least o…

math.CA2026

Applications of Nonlinear Projections to Rectifiable 1-sets

Rosemarie Bongers, Paige Bright, Caleb Marshall +1

Projection theorems in Euclidean space provide a fundamental link between the geometric structure of a set and the size of its lower-dimensional images. For 1-rectifiable sets in $…