An Exceptional Set Estimate for Restricted Projections to Lines in ℝ3
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12220_2023_Article_1456.pdf
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Author(s)
Gan, Shengwen
Guth, Larry
Maldague, Dominique
Date Issued
November 3, 2023
Publisher
Springer US
Citation
The Journal of Geometric Analysis. 2023 Nov 03;34(1):15
Version
Final published version
Abstract
Abstract
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))
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s12220-023-01456-x
