PreprintarXiv licencearXiv
Prescribed projections for a general class of maps and efficient covering by variable plane curves
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.
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BibTeX
@misc{chang2026prescribed,
title = {{Prescribed projections for a general class of maps and efficient covering by variable plane curves}},
author = {Alan Chang and Robert Fraser and Alex McDonald and Mark Meyer and Krystal Taylor},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31602},
eprint = {2609.31602},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31602},
}
RIS
TY - UNPB
TI - Prescribed projections for a general class of maps and efficient covering by variable plane curves
AU - Alan Chang
AU - Robert Fraser
AU - Alex McDonald
AU - Mark Meyer
AU - Krystal Taylor
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31602
UR - https://arxiv.org/abs/2609.31602
AB - 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.
ER -