Work

Prescribed projections for a general class of maps and efficient covering by variable plane curves

Year: 2026

Type: preprint

Abstract: We prove a prescribed projection theorem for any class of non-linear projections defined on open subsets of the plane which satisfies some mild geometric conditions. This generalizes Davies's classic result on prescribed projections for orthogonal projections, as well as a recent result of authors, Chang, McDonald, and Taylor, on a specific class of non-linear projection maps. We also give several geometric applications, including a proof that certain classes of plane curves can be used to cover arbitrary measurable sets with measure zero error.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.31602

Authors: Chang, Alan, Fraser, Robert, McDonald, Alex, Meyer, Mark, Taylor, Krystal

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Ohio State University, Wichita State University, Washington University in St. Louis, Kennesaw State University

Awards: Algebraic Number Fields in Fourier Analysis and Fractal Geometry, Postdoctoral Fellowship: MSPRF: Precise Estimates for Minkowski Sums of Compact Sets, Kakeya sets and rectifiability

OpenAlex ID: W7214681111

Cites: 4

Cited by: 2

Related to: 10