Peter van Hintum

collaborators

3 papers

math.AP2023

Sharp quantitative stability of the Brunn-Minkowski inequality

Alessio Figalli, Peter van Hintum, Marius Tiba

The Brunn-Minkowski inequality states that for bounded measurable sets $A$ and $B$ in $R^{n}$ , we have $∣ A + B ∣^{1/ n} \geq ∣ A ∣^{1/ n} + ∣ B ∣^{1/ n}$ . Also, equality holds if and on…

math.CO2023

Sharp bounds for the Tao-Vu Discrete John's Theorem

Peter van Hintum, Peter Keevash

Tao and Vu showed that every centrally symmetric convex progression $C \subset Z^{d}$ is contained in a generalised arithmetic progression of size $d^{O (d^{2})} # C$ . Berg and…

math.MG2023

The sharp doubling threshold for approximate convexity

Peter van Hintum, Peter Keevash

We show for $A, B \subset R^{d}$ of equal volume and $t \in (0, 1/2]$ that if $∣ t A + (1 - t) B ∣ < (1 + t^{d}) ∣ A ∣$ , then (up to translation) $∣ co (A \cup B) ∣/∣ A ∣$ is bounded. This esta…