“Marstrand’s density theorem for all norms in the plane”
Mercoledì 28 Gennaio 2026 Giovedì 29 Gennaio 2026, ore 12:00 - Aula 2AB45 1BC50 - Andrea Merlo (Universidad del País Vasco)
Abstract
This talk is devoted to generalizing, in the plane, the following classical result of J. Marstrand: if, for a measure, the m-upper and m-lower densities with respect to Euclidean balls coincide almost everywhere, then m is an integer. We will show that, in the plane, this result extends to densities defined with respect to an arbitrary norm. As a consequence, we will prove that Preiss’s theorem holds for every norm in the plane.
These results were obtained in collaboration with G. Del Nin.
