Measure doubling for small sets in SO(3,R).

Let SO(3,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 is an open subset of SO(3,R) with sufficiently small measure, then \mu(A^2) > 3.99 \mu(A). This is joint work with Chieu-Minh Tran (NUS) and Ruixiang Zhang (Berkeley).