From the 1 of 8 linked papers with an AI index.
8 papers
Convex sets with vanishing relative width and the reverse Cheeger inequality
Nicolò Cont, Gian Paolo Leonardi, Giorgio Saracco
The paper extends the reverse Cheeger inequality beyond convex sets, introduces principal widths to measure domain collapse, and shows that sequences of convex bodies with vanishin…
Approximate mean curvature flows of a general varifold, and their limit spacetime Brakke flow
Blanche Buet, Gian Paolo Leonardi, Simon Masnou +1
We propose a construction of mean curvature flows by approximation for very general initial data, in the spirit of the works of Brakke and of Kim & Tonegawa based on the theory of…
Stability of axial free-boundary hyperplanes in circular cones
Gian Paolo Leonardi, Giacomo Vianello
Given an axially-symmetric, -dimensional convex cone , we study the stability of the free-boundary minimal surface obtained by intersecting…
Free-Boundary Monotonicity for Almost-Minimizers of the Relative Perimeter
Gian Paolo Leonardi, Giacomo Vianello
Let be a local almost-minimizer of the relative perimeter in the open set . We prove a free-boundary monotonicity inequality for at a p…
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in
Marco Cicalese, Leonard Kreutz, Gian Paolo Leonardi +1
While the classical Faber-Krahn inequality shows that the ball uniquely minimizes the first Dirichlet eigenvalue of the Laplacian in the continuum, this rigidity may fail in the di…
A Two-Scale Complexity Measure for Deep Learning Models
Massimiliano Datres, Gian Paolo Leonardi, Alessio Figalli +1
We introduce a novel capacity measure 2sED for statistical models based on the effective dimension. The new quantity provably bounds the generalization error under mild assumptions…