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 …

The title is meant as way to honor two great mathematicians that, although never actually
worked together, introduced concepts of convergence that perfectly match each other and …

Consider a BV function on a Riemannian manifold. What is its differential? And what about
the Hessian of a convex function? These questions have clear answers in terms of (co) …

In the framework of quasi‐regular strongly local Dirichlet form (E, D (E)) (E,D(E)) on L 2 (X;
m) L^2(X;m) admitting minimal EE‐dominant measure μ μ, we construct a natural pp‐energy …

The notion of tamed Dirichlet space was proposed by Erbar, Rigoni, Sturm and Tamanini as
a Dirichlet space having a weak form of Bakry-\'Emery curvature lower bounds in distribution …

The notion of tamed Dirichlet space by distributional lower Ricci curvature bounds was
proposed by Erbar, Rigoni, Sturm and Tamanini as the Dirichlet space having a weak form …

We prove that if the Ricci tensor Ric of a geodesically complete Riemannian manifold M,
endowed with the Riemannian distance ρ and the Riemannian measure m, is bounded from …

For $1< p<\infty $, we prove the $ L^ p $-boundedness of the Riesz transform operators on
metric measure spaces with Riemannian Ricci curvature bounded from below, without any …

In the language of $ L^\infty $-modules proposed by Gigli, we introduce a first order calculus
on a topological Lusin measure space $(M,\mathfrak {m}) $ carrying a quasi-regular …

We study the canonical heat flow (H t) t≥ 0 on the cotangent module L 2 (T⁎ M) over an
RCD (K,∞) space (M, d, m), K∈ R. We show Hess–Schrader–Uhlenbrock's inequality and, if …