The purpose of this note is to prove that the flatness of an invariant manifold for a semilinear stochastic partial differential equation driven by Levy processes is at least equal to the number of driving sources with ...

For a fat sub-Riemannian structure, we introduce three canonical Ricci curvatures in the sense of Agrachev–Zelenko–Li. Under appropriate bounds we prove comparison theorems for conjugate lengths, Bonnet–Myers type results ...