Caleb Marshall

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20242026

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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 $…

math.CA2025

Improved Power Laws for the Favard Length Problem in All Dimensions

Caleb Marshall

The Favard length of a compact set in $R^{d}$ is the average one-dimensional Hausdorff measure of its orthogonal projections onto lines. We establish quantitative upper boun…

math.CA2024

Pinned Dot Product Set Estimates

Paige Bright, Caleb Marshall, Steven Senger

We study a variant of the Falconer distance problem for dot products. In particular, for fractal subsets $A \subset R^{n}$ and $a, x \in R^{n}$ , we study sets of the for…

math.CA2024

A Continuum ErdÅs-Beck Theorem

Paige Bright, Caleb Marshall

We prove a version of the ErdÅs--Beck Theorem from discrete geometry for fractal sets in all dimensions. More precisely, let $X \subset R^{n}$ Borel and $k \in [0, n - 1]$ be…

Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint

Applications of Nonlinear Projections to Rectifiable 1-sets

Improved Power Laws for the Favard Length Problem in All Dimensions

Pinned Dot Product Set Estimates

A Continuum ErdÅs-Beck Theorem

A Continuum ErdÅs-Beck Theorem