5 papers
Cheng's eigenvalue comparison on metric measure spaces and applications
G. Bruno De Luca, Nicolò De Ponti, Andrea Mondino +1
Using the localization technique, we prove a sharp upper bound on the first Dirichlet eigenvalue of metric balls in essentially non-branching spaces. Thi…
Global Lipschitz extension preserving the slope
Nicolò De Ponti, Jacopo Somaglia
We show that every real-valued Lipschitz function on a subset of a metric space can be extended to the whole space while preserving the slope and, up to a small error, the global L…
The infimal convolution structure of the Hellinger-Kantorovich distance
Nicolò De Ponti, Giacomo Enrico Sodini, Luca Tamanini
We show that the Hellinger-Kantorovich distance can be expressed as the metric infimal convolution of the Hellinger and the Wasserstein distances, as conjectured by Liero, Mielke,…
Properties of Lipschitz smoothing heat semigroups
Nicolò De Ponti, Giorgio Stefani
We prove several functional and geometric inequalities only assuming the linearity and a quantitative -to-Lipschitz smoothing of the heat semigroup in metric-mea…
Unique continuation at infinity: Carleman estimates on general warped cylinders
Nicolò De Ponti, Stefano Pigola, Giona Veronelli
We obtain a vanishing result for solutions of the inequality that decay to zero along a very general warped cylindrical end of a Riemannian manifold…