dc.contributor.author | Gan, Shengwen | |
dc.contributor.author | Guth, Larry | |
dc.contributor.author | Maldague, Dominique | |
dc.date.accessioned | 2023-11-06T16:46:33Z | |
dc.date.available | 2023-11-06T16:46:33Z | |
dc.date.issued | 2023-11-03 | |
dc.identifier.uri | https://hdl.handle.net/1721.1/152910 | |
dc.description.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
$$E_s(A):=\{\theta \in [0,1]: \dim (\rho _\theta (A))<s\}$$
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.publisher | Springer US | en_US |
dc.relation.isversionof | https://doi.org/10.1007/s12220-023-01456-x | en_US |
dc.rights | Creative Commons Attribution | en_US |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_US |
dc.source | Springer US | en_US |
dc.title | An Exceptional Set Estimate for Restricted Projections to Lines in ℝ3 | en_US |
dc.type | Article | en_US |
dc.identifier.citation | The Journal of Geometric Analysis. 2023 Nov 03;34(1):15 | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | |
dc.identifier.mitlicense | PUBLISHER_CC | |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2023-11-05T04:12:12Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | The Author(s) | |
dspace.embargo.terms | N | |
dspace.date.submission | 2023-11-05T04:12:12Z | |
mit.license | PUBLISHER_CC | |
mit.metadata.status | Authority Work and Publication Information Needed | en_US |