Mathematics

In the first part we will show that on general metric measure spaces, a `Sobolev-like’ first-order differentiation theory is possible, with objects like differential forms and vector fields well defined. 

 

In the second part we will study spaces with Ricci curvature bounded from below, and see that on them the curvature bound makes it possible a second-order calculus, so that, among others, Hessian and covariant derivative are both well defined.