A restricted projection problem for fractal sets in ℝn

Shengwen Gan; Shaoming Guo; Hong Wang

doi:10.4310/CJM.240930233934

A restricted projection problem for fractal sets in ℝⁿ

Shengwen Gan, Shaoming Guo, Hong Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let γ: [-1,1]→ ℝⁿ be a smooth curve that is non-degenerate. Take m ≤ n and a Borel set E ⸦ [0,1]ⁿ, 1sⁿ. We prove that the orthogonal projection of E to the m-th order tangent space of γ at θ ∈ [-1,1].

Original language	English (US)
Pages (from-to)	535-561
Number of pages	27
Journal	Cambridge Journal of Mathematics
Volume	12
Issue number	3
DOIs	https://doi.org/10.4310/CJM.240930233934
State	Published - 2024

ASJC Scopus subject areas

General Mathematics

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10.4310/CJM.240930233934

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abstract = "Let γ: [-1,1]→ ℝn be a smooth curve that is non-degenerate. Take m ≤ n and a Borel set E ⸦ [0,1]n, 1sn. We prove that the orthogonal projection of E to the m-th order tangent space of γ at θ ∈ [-1,1].",

author = "Shengwen Gan and Shaoming Guo and Hong Wang",

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AB - Let γ: [-1,1]→ ℝn be a smooth curve that is non-degenerate. Take m ≤ n and a Borel set E ⸦ [0,1]n, 1sn. We prove that the orthogonal projection of E to the m-th order tangent space of γ at θ ∈ [-1,1].

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A restricted projection problem for fractal sets in ℝⁿ

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