Title: The Hellinger-Kantorovich metric measure geometry on spaces of measures
Abstract: We prove that the space of (non-negative and finite Borel) measures on a complete Riemannian manifold endowed with the Hellinger-Kantorovich distance is universally infinitesimally Hilbertian and that the class of cylinder functions is dense in energy. We endow the aforementioned metric space with its canonical reference measure (the multiplicative infinite-dimensional Lebesgue measure) and we identify its Dirichlet form with the Cheeger energy of the metric-measure space. This work has been done in collaboration with Lorenzo Dello Schiavo.
