Caltech/UCLA/USC Joint Analysis Seminar

Let x be a point in the plane, the radial projection \pi_x is defined by pi_x(y)= \frac{x-y}{|x-y|} for any y\neq x\in \mathbb{R}^2. Suppose that X is a Borel set in the plane and is not contained in any line, then we show that there exists a point x\in X such that \pi_x (X) has dimension equals to \min \{ \dim_H X, 1\}. This is joint work with Tuomas Orponen and Pablo Shmerkin.