Brownian motion speaks analysis and geometry in a beautiful connection with bounded variation (BV) measures and the perimeter of sets. In this talk we will review that relation in the Euclidean setting through the work of Cacciopoli, de Giorgi and Ledoux, and from there move to more general metric measure spaces. Moving beyond the Euclidean setting we will discuss recent developments in the context of fractals, and in particular an oscillatory phenomenon that occurs when the underlying space is an unbounded planar nested fractal. Based on joint work with Fabrice Baudoin.

Imparte
Patricia Alonso Ruiz
Department of Mathematics
Texas A&M University