Tuomas Orponen: Sharpening Marstrand’s projection theorem in R^3

Marstrand’s projection theorem in R^3 states that the dimension of 1-dimensional sets is a.s. preserved, when they are projected to lines through the origin. Here “a.s.” refers to the surface measure on the 2-sphere. I will discuss recent work with A. Käenmäki and L. Venieri, where we showed that the result remains true, if “a.s.” refers, instead, to length measure on certain curves on the 2-sphere.