Mathematics

In this seminar, we review the theory of Gradient Flows in the framework of convex and lower semicontinuous functionals on CAT(0)-spaces and prove that they can be characterized by the same differential inclusion $y_t'\in-\partial^-E(y_t)$ one uses in the smooth setting and more precisely that $y_t'$ selects the element of minimal norm in $-\partial^-E(y_t)$.

We then apply such result to the Korevaar-Schoen energy functional on the space of $L^2$ and CAT(0) valued maps. A definition of Laplacian is then derived and basic properties are then studied.