Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Classical Analysis and ODEs

arXiv:2207.02259 (math)
[Submitted on 5 Jul 2022 (v1), last revised 25 Oct 2024 (this version, v3)]

Title:A Furstenberg-type problem for circles, and a Kaufman-type restricted projection theorem in $\mathbb{R}^3$

Authors:Malabika Pramanik, Tongou Yang, Joshua Zahl
View PDF HTML (experimental)
Abstract:We resolve a conjecture of Fässler and Orponen on the dimension of exceptional projections to one-dimensional subspaces indexed by a space curve in $\mathbb{R}^3$. We do this by obtaining sharp $L^p$ bounds for a variant of the Wolff circular maximal function over fractal sets for a class of $C^2$ curves related to Sogge's cinematic curvature condition. A key new tool is the use of lens cutting techniques from discrete geometry.
Comments: 37 pages, 3 figures. v3: final version, to appear in Amer. J. Math
Subjects: Classical Analysis and ODEs (math.CA); Metric Geometry (math.MG)
Cite as: arXiv:2207.02259 [math.CA]
  (or arXiv:2207.02259v3 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.2207.02259

Submission history

From: Joshua Zahl [view email]
[v1] Tue, 5 Jul 2022 18:42:41 UTC (352 KB)
[v2] Sat, 3 Sep 2022 00:04:50 UTC (43 KB)
[v3] Fri, 25 Oct 2024 21:25:53 UTC (44 KB)
Full-text links:

Access Paper:

license icon view license
Current browse context:
math.CA
< prev   |   next >
new | recent | 2022-07
Change to browse by:
math
math.MG

References & Citations

1 blog link

(what is this?)
export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)