24 citations · 168 across the 32 of their papers we have counts for
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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…
A Vertex-Skipping property for almost-minimizers of the relative perimeter in convex sets
Gian Paolo Leonardi, Giacomo Vianello
Given a convex domain and an almost-minimizer of the relative perimeter in , we prove that the closure of does not contain vert…
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…