Hong Wang

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math.CA2025

Sticky Kakeya sets and the sticky Kakeya conjecture

Hong Wang, Joshua Zahl

A Kakeya set is a compact subset of $R^{n}$ that contains a unit line segment pointing in every direction. The Kakeya conjecture asserts that such sets must have Hausdorff a…

math.CA2025

Furstenberg sets estimate in the plane

Kevin Ren, Hong Wang

We fully resolve the Furstenberg set conjecture in $R^{2}$ , that a $(s, t)$ -Furstenberg set has Hausdorff dimension $\geq min (s + t, \frac{3 s + t}{2}, s + 1)$ . As a result, we obt…

math.CA2024

Some sharp inequalities of Mizohata--Takeuchi-type

Anthony Carbery, Marina Iliopoulou, Hong Wang

Let $I^£$ be a strictly convex, compact patch of a $C^{2}$ hypersurface in $R^{n}$ , with non-vanishing Gaussian curvature and surface measure $d I ¨ $ induced by the Lebesgue meas…

math.CA2024

On the distance sets spanned by sets of dimension $d /2$ in $R^{d}$

Pablo Shmerkin, Hong Wang

We establish the dimension version of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors-regular sets) in all ambient…

Sticky Kakeya sets and the sticky Kakeya conjecture

Furstenberg sets estimate in the plane

Some sharp inequalities of Mizohata--Takeuchi-type

On the distance sets spanned by sets of dimension d/2 in Rd

On the distance sets spanned by sets of dimension $d /2$ in $R^{d}$