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Non-branching properties of Regular Lagrangian Flows and well posedness of the continuity equation in the class of nonnegative solutions
Luigi Ambrosio, Stefano Bianchini, Federico Renzi +1
In this paper we deal with the theory of Regular Lagrangian Flows, as initiated in [29] and axiomatized in [2]. In the first part of the paper we show in Theorem 4.3 (see also Coro…
Stability of local Riemannian Ricci curvature lower bounds
Luigi Ambrosio, Francesco Nobili, Federico Renzi +1
We establish the stability of local Riemannian Ricci curvature lower bounds along Gromov-Hausdorff convergence. A central part of our analysis is devoted to showing the stability o…
Renormalization of contact vector fields with horizontal Sobolev regularity in Heisenberg groups
Luigi Ambrosio, Gianluca Somma, Simone Verzellesi +1
In this paper we obtain the well-posedness of the transport and continuity equations in the Heisenberg groups for a class of contact vector fields , under…