5 citations · 16 across the 13 of their papers we have counts for
11 papers · 1 filter
On the equivalence of the integrability obstructions for transitive Lie algebroids
Paolo Antonini, Alessio Giannotta
The integrability problem for transitive Lie algebroids can be looked at from different perspectives, revealing an interplay between cohomological methods and homotopical construct…
Optimal transport between algebraic hypersurfaces
Paolo Antonini, Fabio Cavalletti, Antonio Lerario
What is the optimal way to deform a projective hypersurface into another one? In this paper we will answer this question adopting the point of view of measure theory, introducing t…
Geometry of Grassmannians and optimal transport of quantum states
Paolo Antonini, Fabio Cavalletti
Let be a separable Hilbert space. We prove that the Grassmannian of the finite dimensional subspaces of is an Alexandrov space…
The injectivity radius of Lie manifolds
Paolo Antonini, Guido De Philippis, Nicola Gigli
We prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive
Integrable lifts for transitive Lie algebroids
Iakovos Androulidakis, Paolo Antonini
Inspired by the work of Molino, we show that the integrability obstruction for transitive Lie algebroids can be made to vanish by adding extra dimensions. In particular, we prove t…
The Calderon projection over C* algebras
Paolo Antonini
We construct the Calderon projection on the space of Cauchy datas for a twisted Dirac operator in the Mischenko--Fomenko pseudodifferential calculus for operators acting on bundles…