Metric measure spaces with synthetic Ricci bounds have attracted great interest in recent
years, accompanied by spectacular breakthroughs and deep new insights. In this survey, I …

We give a general description of the dual of the pullback of a normed module. Ours is the
natural generalization to the context of modules of the well-known fact that the dual of the …

Abstract We extend Korevaar–Schoen's theory of metric valued Sobolev maps to cover the
case of the source space being an RCD RCD space. In this situation it appears that no …

For an harmonic map $ u $ from a domain $ U\subset {\rm X} $ in an ${\sf RCD}(K, N) $
space ${\rm X} $ to a ${\sf CAT}(0) $ space ${\rm Y} $ we prove the Lipschitz estimate\[{\rm …

In this paper we study the structure theory of normed modules, which have been introduced
by Gigli. The aim is twofold: to extend von Neumann's theory of liftings to the framework of …

We show that, given a metric space (Y, d)(Y, d) of curvature bounded from above in the
sense of Alexandrov, and a positive Radon measure μ μ on YY giving finite mass to …

We establish Lipschitz regularity of harmonic maps from RCD (K, N) metric measure spaces
with lower Ricci curvature bounds and dimension upper bounds in synthetic sense with …

Infinitesimal Hilbertianity of Weighted Riemannian Manifolds Page 1 Canad. Math. Bull. Vol.
63 ( ), pp. – http://dx.doi.org/. /S ©Canadian Mathematical Society Infinitesimal Hilbertianity of …

We review the theory of Gradient Flows in the framework of convex and lower
semicontinuous functionals on CAT (κ)-spaces and prove that they can be characterized by …

Abstract We develop Korevaar–Schoen's theory of directional energies for metric-valued
Sobolev maps in the case of RCD RCD source spaces; to do so we crucially rely on …