135 citations · 217 across the 18 of their papers we have counts for
23 papers · 1 filter
Minimizing cones for fractional capillarity problems
Serena Dipierro, Francesco Maggi, Enrico Valdinoci
We consider a fractional version of Gauss capillarity energy. A suitable extension problem is introduced to derive a boundary monotonicity formula for local minimizers of this frac…
Smoothness of collapsed regions in a capillarity model for soap films
Darren King, Francesco Maggi, Salvatore Stuvard
We study generalized minimizers in the soap film capillarity model introduced in [arXiv:1807.05200,arXiv:1907.00551]. Collapsed regions of generalized minimizers are shown to be sm…
Symmetry and Rigidity of Minimal Surfaces with Plateau-like Singularities
Jacob Bernstein, Francesco Maggi
By employing the method of moving planes in a novel way we extend some classical symmetry and rigidity results for smooth minimal surfaces to surfaces that have singularities of th…
Collapsing and the convex hull property in a soap film capillarity model
Darren King, Francesco Maggi, Salvatore Stuvard
Soap films hanging from a wire frame are studied in the framework of capillarity theory. Minimizers in the corresponding variational problem are known to consist of positive volume…
Plateau's problem as a singular limit of capillarity problems
Darren King, Francesco Maggi, Salvatore Stuvard
Soap films at equilibrium are modeled, rather than as surfaces, as regions of small total volume through the introduction of a capillarity problem with a homotopic spanning conditi…
Soap films with gravity and almost-minimal surfaces
Francesco Maggi, Antonello Scardicchio, Salvatore Stuvard
Motivated by the study of the equilibrium equations for a soap film hanging from a wire frame, we prove a compactness theorem for surfaces with asymptotically vanishing mean curvat…
Asymptotic expansions of the contact angle in nonlocal capillarity problems
Serena Dipierro, Francesco Maggi, Enrico Valdinoci
We consider a family of nonlocal capillarity models, where surface tension is modeled by exploiting the family of fractional interaction kernels , with and…
A bridge between Sobolev and Escobar inequalities and beyond
Francesco Maggi, Robin Neumayer
The classical Sobolev and Escobar inequalities are embedded into the same one-parameter family of sharp trace-Sobolev inequalities on half-spaces. Equality cases are characterized…
Capillarity problems with nonlocal surface tension energies
Francesco Maggi, Enrico Valdinoci
We explore the possibility of modifying the classical Gauss free energy functional used in capillarity theory by considering surface tension energies of nonlocal type. The correspo…
A quantitative analysis of metrics on with almost constant positive scalar curvature, with applications to fast diffusion flows
Giulio Ciraolo, Alessio Figalli, Francesco Maggi
We prove a quantitative structure theorem for metrics on that are conformal to the flat metric, have almost constant positive scalar curvature, and cannot concentrat…
The sharp quantitative Euclidean concentration inequality
Alessio Figalli, Francesco Maggi, Connor Mooney
The Euclidean concentration inequality states that, among sets with fixed volume, balls have -neighborhoods of minimal volume for every . On an arbitrary set, the deviation…
On the shape of capillarity droplets in a container
Francesco Maggi, Cornelia Mihaila
We provide a quantitative description of global minimizers of the Gauss free energy for a liquid droplet bounded in a container in the small volume regime.
Improved convergence theorems for bubble clusters. II. The three-dimensional case
Gian Paolo Leonardi, Francesco Maggi
Given a sequence of almost-minimizing clusters in which converges in to a limit cluster we prove the existence of $C^…
On the shape of compact hypersurfaces with almost constant mean curvature
Giulio Ciraolo, Francesco Maggi
The distance of an almost constant mean curvature boundary from a finite family of disjoint tangent balls with equal radii is quantitatively controlled in terms of the oscillation…
Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature
Giulio Ciraolo, Alessio Figalli, Francesco Maggi +1
We prove that the boundary of a (not necessarily connected) bounded smooth set with constant nonlocal mean curvature is a sphere. More generally, and in contrast with what happens…
A sharp quantitative version of Hales' isoperimetric honeycomb theorem
Marco Caroccia, Francesco Maggi
We prove a sharp quantitative version of Hales' isoperimetric honeycomb theorem by exploiting a quantitative isoperimetric inequality for polygons and an improved convergence theor…
A direct approach to Plateau's problem
Camillo De Lellis, Francesco Ghiraldin, Francesco Maggi
We provide a compactness principle which is applicable to different formulations of Plateau's problem in codimension one and which is exclusively based on the theory of Radon measu…
Improved convergence theorems for bubble clusters. I. The planar case
Marco Cicalese, Gian Paolo Leonardi, Francesco Maggi
We describe a quantitative construction of almost-normal diffeomorphisms between embedded orientable manifolds with boundary to be used in the study of geometric variational proble…
Dimensional estimates for singular sets in geometric variational problems with free boundaries
Guido De Philippis, Francesco Maggi
We show that singular sets of free boundaries arising in codimension one anisotropic geometric variational problems are -negligible, where is the ambient spa…
Isoperimetry and stability properties of balls with respect to nonlocal energies
Alessio Figalli, Nicola Fusco, Francesco Maggi +2
We obtain a sharp quantitative isoperimetric inequality for nonlocal -perimeters, uniform with respect to bounded away from . This allows us to address local and global m…
Rigidity of equality cases in Steiner's perimeter inequality
Filippo Cagnetti, Maria Colombo, Guido De Philippis +1
Characterization results for equality cases and for rigidity of equality cases in Steiner's perimeter inequality are presented. (By rigidity, we mean the situation when all equalit…
Essential connectedness and the rigidity problem for Gaussian symmetrization
Filippo Cagnetti, Maria Colombo, Guido De Philippis +1
We provide a geometric characterization of rigidity of equality cases in Ehrhard's symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new…
Sharp stability inequalities for planar double bubbles
Marco Cicalese, Gian Paolo Leonardi, Francesco Maggi
In this paper we address the global stability problem for double-bubbles in the plane. This is accomplished by combining the "improved convergence theorem" for planar clusters deve…