PreprintCC0arXiv
Positive measure for restricted projections along smooth non-degenerate curves
Abstract
Let 1≤ m<n, and let γ:[0,1]→ℝn be a smooth non-degenerate curve. For θ∈[0,1], set Vθ := span {γ'(θ),…,γ(m)(θ)}, and let πθ denote the orthogonal projection onto Vθ. We prove that if E⊂ℝn is a Borel set with dimHE>m, then ℋm(πθ(E))>0 for almost every θ∈[0,1].
Related
- On restricted projections to planes in ℝ3
- Spread-out Furstenberg sets II: general configurations and fractal restricted projections
- On the Hausdorff measure of projections of self-similar sets
- The Hodge-to-de Rham spectral sequence can be arbitrarily non-degenerate in positive characteristic
- A mass-type invariant for smooth metric measure spaces and its relation with the fractional Yamabe problem
BibTeX
@misc{jeon2026positive,
title = {{Positive measure for restricted projections along smooth non-degenerate curves}},
author = {Seonghun Jeon and Changkeun Oh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.21822},
eprint = {2608.21822},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.21822},
note = {CC0},
}
RIS
TY - UNPB
TI - Positive measure for restricted projections along smooth non-degenerate curves
AU - Seonghun Jeon
AU - Changkeun Oh
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2608.21822
UR - https://arxiv.org/abs/2608.21822
AB - Let 1≤ m<n, and let γ:[0,1]→ℝ^n be a smooth non-degenerate curve. For θ∈[0,1], set V_θ := span {γ'(θ),…,γ^(m)(θ)}, and let π_θ denote the orthogonal projection onto V_θ. We prove that if E⊂ℝ^n is a Borel set with dim_HE>m, then ℋ^m(π_θ(E))>0 for almost every θ∈[0,1].
ER -