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dc.contributor.authorGan, Shengwen
dc.contributor.authorGuth, Larry
dc.contributor.authorMaldague, Dominique
dc.date.accessioned2023-11-06T16:46:33Z
dc.date.available2023-11-06T16:46:33Z
dc.date.issued2023-11-03
dc.identifier.urihttps://hdl.handle.net/1721.1/152910
dc.description.abstractAbstract Let $$\gamma :[0,1]\rightarrow \mathbb S^{2}$$ γ : [ 0 , 1 ] → S 2 be a non-degenerate curve in $$\mathbb R^3$$ R 3 , that is to say, $$\det \big (\gamma (\theta ),\gamma '(\theta ),\gamma ''(\theta )\big )\ne 0$$ det ( γ ( θ ) , γ ′ ( θ ) , γ ′ ′ ( θ ) ) ≠ 0 . For each $$\theta \in [0,1]$$ θ ∈ [ 0 , 1 ] , let $$l_\theta =\text {span}(\gamma (\theta ))$$ l θ = span ( γ ( θ ) ) and $$\rho _\theta :\mathbb R^3\rightarrow l_\theta $$ ρ θ : R 3 → l θ be the orthogonal projections. We prove an exceptional set estimate. For any Borel set $$A\subset \mathbb R^3$$ A ⊂ R 3 and $$0\le s\le 1$$ 0 ≤ s ≤ 1 , define $$E_s(A):=\{\theta \in [0,1]: \dim (\rho _\theta (A))<s\}$$ E s ( A ) : = { θ ∈ [ 0 , 1 ] : dim ( ρ θ ( A ) ) < s } . We have $$\dim (E_s(A))\le \max \{0,1+\frac{s-\dim (A)}{2}\}$$ dim ( E s ( A ) ) ≤ max { 0 , 1 + s - dim ( A ) 2 } .en_US
dc.publisherSpringer USen_US
dc.relation.isversionofhttps://doi.org/10.1007/s12220-023-01456-xen_US
dc.rightsCreative Commons Attributionen_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.sourceSpringer USen_US
dc.titleAn Exceptional Set Estimate for Restricted Projections to Lines in ℝ3en_US
dc.typeArticleen_US
dc.identifier.citationThe Journal of Geometric Analysis. 2023 Nov 03;34(1):15en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
dc.identifier.mitlicensePUBLISHER_CC
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2023-11-05T04:12:12Z
dc.language.rfc3066en
dc.rights.holderThe Author(s)
dspace.embargo.termsN
dspace.date.submission2023-11-05T04:12:12Z
mit.licensePUBLISHER_CC
mit.metadata.statusAuthority Work and Publication Information Neededen_US


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