works on
global differential calculus 1levi-civita connection 1optimal transport 1otto metric 1riemannian geometry 1wasserstein spaces 1

From the 1 of 6 linked papers with an AI index.

collaborators

6 papers

math.DG2026

A 'global' Perspective on the Differential Geometry of Wasserstein Spaces

Lorenzo Dello Schiavo, Andrea Pinamonti

The paper builds a global differential calculus on the L²‑Wasserstein space over a closed Riemannian manifold, defining geometric structures such as a torsion‑free connection and R…

math.FA2025

Non-bilinear Dirichlet Functionals: Markovianity, locality, invariance

Giovanni Brigati, Lorenzo Dello Schiavo

We present in a unified setting the foundations for a theory of non-bilinear Dirichlet functionals on Hilbert spaces. We prove known and new equivalences between non-linear semigro…

math.PR2025

Massive Particle Systems, Wasserstein Brownian Motions, and the Dean-Kawasaki Equation

Lorenzo Dello Schiavo

We develop a unifying theory for four different objects: (1) infinite systems of interacting massive particles; (2) solutions to the Dean-Kawasaki equation with singular drift and…

math.FA2025

Gradient flows of -convex functions with negative

Lorenzo Dello Schiavo, Mattia Magnabosco, Chiara Rigoni

We discuss -convexity and gradient flows for -convex functionals on metric spaces, in the case of real and negative . In this generality, it is necessary to co…

math.FA2025

The Hellinger-Kantorovich metric measure geometry on spaces of measures

Lorenzo Dello Schiavo, Giacomo Enrico Sodini

Let be a Riemannian manifold with Riemannian distance , and be the space of all non-negative Borel measures on , endowed with the Hellinge…

math.PR2025

Ill-posedness of the pure-noise Dean-Kawasaki equation

Lorenzo Dello Schiavo, Vitalii Konarovskyi

We prove that the Dean-Kawasaki-type stochastic partial differential equation with vector-valu…