13 citations · 38 across the 11 of their papers we have counts for
12 papers
Can you hear the Planck mass?
G. Bruno De Luca, Nicolò De Ponti, Andrea Mondino +1
For the Laplacian of an -Riemannian manifold , the Weyl law states that the -th eigenvalue is asymptotically proportional to , where is the volume of .…
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.…
Pleijel nodal domain theorem in non-smooth setting
Nicolò De Ponti, Sara Farinelli, Ivan Yuri Violo
We prove the Pleijel theorem in non-collapsed RCD spaces, providing an asymptotic upper bound on the number of nodal domains of Laplacian eigenfunctions. As a consequence, we obtai…
Harmonic functions and gravity localization
G. Bruno De Luca, Nicolò De Ponti, Andrea Mondino +1
In models with extra dimensions, matter particles can be easily localized to a 'brane world', but gravitational attraction tends to spread out in the extra dimensions unless they a…
Gravity from thermodynamics: optimal transport and negative effective dimensions
G. Bruno De Luca, Nicolò De Ponti, Andrea Mondino +1
We prove an equivalence between the classical equations of motion governing vacuum gravity compactifications (and more general warped-product spacetimes) and a concavity property o…
Cheeger bounds on spin-two fields
G. Bruno De Luca, Nicolò De Ponti, Andrea Mondino +1
We consider gravity compactifications whose internal space consists of small bridges connecting larger manifolds, possibly noncompact. We prove that, under rather general assumptio…
Indeterminacy estimates, eigenfunctions and lower bounds on Wasserstein distances
Nicolò De Ponti, Sara Farinelli
In the paper we prove two inequalities in the setting of spaces using similar techniques. The first one is an indeterminacy estimate involving the -Wassers…
Entropy-Transport distances between unbalanced metric measure spaces
Nicoló De Ponti, Andrea Mondino
Inspired by the recent theory of Entropy-Transport problems and by the -distance of Sturm on normalised metric measure spaces, we define a new class of complete and sep…
The equality case in Cheeger's and Buser's inequalities on spaces
Nicolò De Ponti, Andrea Mondino, Daniele Semola
We prove that the sharp Buser's inequality obtained in the framework of spaces by the first two authors is rigid, i.e. equality is obtained if and only if…
Wasserstein stability of porous medium-type equations on manifolds with Ricci curvature bounded below
Nicolò De Ponti, Matteo Muratori, Carlo Orrieri
Given a complete, connected Riemannian manifold with Ricci curvature bounded from below, we discuss the stability of the solutions of a porous medium-type equation…
Concentration on submanifolds of positively curved homogeneous spaces
Nicolò De Ponti
A classical result of Milman roughly states that every Lipschitz function on is almost constant on a sufficiently high-dimensional sphere $\mathbb{S}^m\subset \mathb…