A paper titled “Sticky Kakeya Sets and the Sticky Kakeya Conjecture” by Joshua Zahl, Chair Professor at the Chern Institute of Mathematics, Nankai University, and his collaborator Wang Hong, a jointly appointed professor at New York University’s Courant Institute of Mathematical Sciences and France’s Institut des Hautes Études Scientifiques, has been published online in the internationally top-tier mathematics journal, Journal of the American Mathematical Society. This marks the first paper published by Joshua Zahl since joining Nankai University in June this year.

A Kakeya set is a compact subset of Euclidean space that contains a unit line segment pointing in every direction. The Kakeya set conjecture says that every Kakeya set in n dimensional Euclidean space has Hausdorff and Minkowski dimension n. This paper proves a key special case of the Kakeya set conjecture in three dimensions---it proves the conjecture for a special class of Kakeya sets called sticky Kakeya sets. In brief, a Kakeya set is sticky if lines pointing in nearby directions usually occupy similar locations in space. The results from this paper were an important ingredient in the authors' later work that fully resolved the Kakeya set conjecture in three dimensions.

Joshua Zahl at the Chern Institute of Mathematics, Nankai University

Link to the paper:

https://www.ams.org/journals/jams/0000-000-00/S0894-0347-2025-01067-8/

（Edited and translated by Nankai News Team.)