We establish a duality between Lp-Wasserstein control and Lq-gradient estimate in a
general framework. Our result extends a known result for a heat flow on a Riemannian …

We try to provide a visual introduction to some objects used in Riemannian geometry:
parallel transport, sectional curvature, Ricci curvature, Bianchi identities... We then explain …

We study the heat equation on time‐dependent metric measure spaces (as well as the dual
and the adjoint heat equation) and prove existence, uniqueness, and regularity. Of particular …

Given a metric measure space (X, d, m) and a lower semicontinuous, lower bounded
function k: X→ R, we prove the equivalence of the synthetic approaches to Ricci curvature at …

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 …

We study the problem of non-explosion of diffusion processes on a manifold with time-
dependent Riemannian metric. In particular we obtain that Brownian motion cannot explode …

We construct a family of SDEs with smooth coefficients whose solutions select a reflected
Brownian flow as well as a corresponding stochastic damped transport process (W_t), the …

We devise a generalisation of the energy momentum-method for studying the stability of non-
autonomous Hamiltonian systems with a Lie group of Hamiltonian symmetries. A …

We show that on a manifold whose Riemannian metric evolves under backwards Ricci flow
two Brownian motions can be coupled in such a way that their normalized L-distance is a …

The duality in Bakry–Émery's gradient estimates and Wasserstein controls for heat
distributions is extended to that in refined estimates in a high generality. As a result, we find …