24 citations · 168 across the 32 of their papers we have counts for
37 papers
Convex sets with vanishing relative width and the reverse Cheeger inequality
Nicolò Cont, Gian Paolo Leonardi, Giorgio Saracco
We study the reverse Cheeger inequality, which bounds from above the ratio of the first Dirichlet Laplacian eigenvalue to the square of the Cheeger constant. We first extend this i…
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…
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…
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 $Ω…
Measures in the dual of : perimeter bounds and relations with divergence-measure fields
Giovanni E. Comi, Gian Paolo Leonardi
We analyze some properties of the measures in the dual of the space , by considering (signed) Radon measures satisfying a perimeter bound condition, which means that the absolu…
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 poi…