curved kakeya problems 1Hausdorff dimension 1incidence geometry 1projective geometry of paths 1spray geometry 1
From the 1 of 2 linked papers with an AI index.
2 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.DG2025
Parametric inequalities and Weyl law for the volume spectrum
Larry Guth, Yevgeny Liokumovich
We show that the Weyl law for the volume spectrum in a compact Riemannian manifold conjectured by Gromov can be derived from parametric generalizations of two famous inequalities:…