The dimension of projections induced by a curve

TL;DR

This paper addresses a key question in fractal geometry by analyzing how the Hausdorff dimension of a set behaves when projected onto lines determined by a curve, settling a previously open problem.

Contribution

It provides a definitive answer to Fassler and Orponen's question about the dimension of projections onto line families induced by a curve.

Findings

Confirmed the behavior of Hausdorff dimension under such projections

Resolved an open problem in fractal geometry

Established new results on projections induced by curves

Abstract

The behavior of the Hausdorff dimension of a set when projected onto a subspace is a fundamental question in fractal geometry. In this paper, we settle a question of Fassler and Orponen concerning the dimension of a set when projected onto a family of lines induced by a curve.