the hybrid MaDS seminar: AMV Laplacian

AMV Laplacian

As well-known, the Laplacian in Rn is the sum of the unmixed partial derivatives of order 2. This definition requires a second-order differential calculus. In this talk, I will present some aspects of the Asymptotic Mean Value (AMV) Laplacian which does not need any differentiable structure to be defined. Formally, this operator can be introduced in any metric measure space. I will focus on the key examples of Carnot groups and sub-Riemannian manifolds.