12 citations · 24 across the 15 of their papers we have counts for
20 papers
Regularity of varifolds with bounded anisotropic first variation
Antonio De Rosa, Benjy Firester, Raphael Tsiamis
We prove an -regularity theorem for -varifolds with mean curvature in , , with respect to an anisotropic integrand satisfying a Michael-Simon inequality a…
Lectures on Existence and Regularity of Anisotropic Minimal Surfaces
Antonio De Rosa
For several natural phenomena, the use of the surface area functional is a first approximation. In order to capture microstructures, numerous models in applied sciences employ dire…
On the power of linear programming for K-means clustering
Antonio De Rosa, Aida Khajavirad, Yakun Wang
In [SIAM J. Optim., 2022], the authors introduced a new linear programming (LP) relaxation for K-means clustering. In this paper, we further investigate both theoretical and comput…
Construction of fillings with prescribed Gaussian image and applications
Antonio De Rosa, Yucong Lei, Robert Young
We construct -dimensional polyhedral chains such that the distribution of tangent planes is close to a prescribed measure on the Grassmannian and the chains are either cycles (i…
Local Minimizers of the Anisotropic Isoperimetric Problem on Closed Manifolds
Antonio De Rosa, Robin Neumayer
Local minimizers for the anisotropic isoperimetric problem in the small-volume regime on closed Riemannian manifolds are shown to be geodesically convex and small smooth perturbati…
Boundary regularity for anisotropic minimal Lipschitz graphs
Antonio De Rosa, Reinaldo Resende
We prove that -dimensional Lipschitz graphs in any codimension with boundary and anisotropic mean curvature bounded in , , are regular at every boundary po…
The double and triple bubble problem for stationary varifolds: the convex case
Antonio De Rosa, Riccardo Tione
We characterize the critical points of the double bubble problem in and the triple bubble problem in , in the case the bubbles are convex.
Explicit convex hull description of bivariate quadratic sets with indicator variables
Antonio De Rosa, Aida Khajavirad
We consider the nonconvex set , which is closely related to the feasible region of several diff…
The anisotropic Min-Max theory: Existence of anisotropic minimal and CMC surfaces
Guido De Philippis, Antonio De Rosa
We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth -dimensional Riemannian manifo…
Efficient Joint Object Matching via Linear Programming
Antonio De Rosa, Aida Khajavirad
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task…
Regularity for graphs with bounded anisotropic mean curvature
Antonio De Rosa, Riccardo Tione
We prove that -dimensional Lipschitz graphs with anisotropic mean curvature bounded in , , are regular almost everywhere in every dimension and codimension. This provi…
The ratio-cut polytope and K-means clustering
Antonio De Rosa, Aida Khajavirad
We introduce the ratio-cut polytope defined as the convex hull of ratio-cut vectors corresponding to all partitions of points in into at most clusters. This p…
Stability of optimal traffic plans in the irrigation problem
Maria Colombo, Antonio de Rosa, Andrea Marchese +2
We prove the stability of optimal traffic plans in branched transport. In particular, we show that any limit of optimal traffic plans is optimal as well. This is the Lagrangian cou…
On the well-posedness of branched transportation
Maria Colombo, Antonio De Rosa, Andrea Marchese
We show in full generality the stability of optimal traffic paths in branched transport: namely we prove that any limit of optimal traffic paths is optimal as well. This solves an…
Absence of bubbling phenomena for non convex anisotropic nearly umbilical and quasi Einstein hypersurfaces
Antonio De Rosa, Stefano Gioffrè
We prove that, for every closed (not necessarily convex) hypersurface in and every , the -norm of the trace-free part of the anisotropic second fun…
Existence results for minimizers of parametric elliptic functionals
Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin
We prove a compactness principle for the anisotropic formulation of the Plateau problem in any codimension, in the same spirit of the previous works of the authors \cite{DelGhiMag,…
Minimization of anisotropic energies in classes of rectifiable varifolds
Antonio De Rosa
We consider the minimization problem of an anisotropic energy in classes of -rectifiable varifolds in , closed under Lipschitz deformations and encoding a suitable…
Rectifiability of varifolds with locally bounded first variation with respect to anisotropic surface energies
Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin
We extend Allard's celebrated rectifiability theorem to the setting of varifolds with locally bounded first variation with respect to an anisotropic integrand. In particular, we id…
A direct approach to the anisotropic Plateau problem
Camillo De Lellis, Antonio De Rosa, Francesco Ghiraldin
We prove a compactness principle for the anisotropic formulation of the Plateau problem in codimension one, along the same lines of previous works of the authors [DGM14, DPDRG15].…
A direct approach to Plateau's problem in any codimension
Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin
This paper aims to propose a direct approach to solve the Plateau's problem in codimension higher than one. The problem is formulated as the minimization of the Hausdorff measure a…