Measure growth of small sets in \(\mathrm{SO}(3,\mathbb{R})\)

21.03.2023 15:00 - 17:00

Tran Chieu Minh (NU Singapore)

Let \(\mathrm{SO}(3,\mathbb{R})\) be the 3D-rotation group equipped with the real-manifold topology and the normalized Haar measure \(\mu\). Confirming a conjecture by Breuillard and Green, we show that if \(A \subseteq \mathrm{SO}(3,\mathbb{R})\) is open and has sufficiently small measure, then \( \mu(A^2) > 3.99 \mu(A)\). We also show a more general result for the product of two sets, which can be seen as a Brunn-Minkowski-type inequality for sets with small measure in \(\mathrm{SO}(3,\mathbb{R})\). (Joint with Yifan Jing and Ruixiang Zhang)


G. Arzhantseva, Ch. Cashen


BZ 9, 9. OG, OMP1