curved kakeya problems 1Hausdorff dimension 1incidence geometry 1projective geometry of paths 1spray geometry 1
From the 1 of 3 linked papers with an AI index.
3 papers
math.CA2026
Curved Kakeya problems and the projective geometry of paths
Shaoming Guo, Larry Guth, Arian Nadjimzadah +2
The paper develops a general framework for curved Kakeya problems using spray geometry and the projective geometry of paths, characterizing when Wolff's hairbrush argument applies…
math.CA2026
New curved Kakeya estimates
Arian Nadjimzadah
We prove that for an open class of translation-invariant Hörmander-type phase functions, the corresponding curved Kakeya sets in have Hausdorff dimension at least $(1…
math.CA2026
Bourgain's condition, sticky Kakeya, and new examples
Arian Nadjimzadah
We prove that in all dimensions at least 3 and for any Hörmander-type phase function satisfying Bourgain's condition, the sticky case of the corresponding curved Kakeya conjecture…