A. De Rosa

activity

20152026

most citedAbsence of bubbling phenomena for non convex anisotropic nearly umbilical and quasi Einstein hypersurfaces

12 citations · 24 across the 15 of their papers we have counts for

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15 papers · 1 filter

math.AP2026

Regularity of varifolds with bounded anisotropic first variation

Antonio De Rosa, Benjy Firester, Raphael Tsiamis

We prove an $ε$ -regularity theorem for $m$ -varifolds with mean curvature in $L^{p}$ , $p > m$ , with respect to an anisotropic integrand satisfying a Michael-Simon inequality a…

math.AP2026

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…

math.AP2024

Construction of fillings with prescribed Gaussian image and applications

Antonio De Rosa, Yucong Lei, Robert Young

We construct $d$ -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…

math.AP2023

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…

math.AP2023★ 1 cited

Boundary regularity for anisotropic minimal Lipschitz graphs

Antonio De Rosa, Reinaldo Resende

We prove that $m$ -dimensional Lipschitz graphs in any codimension with $C^{1, α}$ boundary and anisotropic mean curvature bounded in $L^{p}$ , $p > m$ , are regular at every boundary po…

math.AP2023★ 1 cited

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 $R^{n}$ and the triple bubble problem in $R^{3}$ , in the case the bubbles are convex.

math.AP2020

Regularity for graphs with bounded anisotropic mean curvature

Antonio De Rosa, Riccardo Tione

We prove that $m$ -dimensional Lipschitz graphs with anisotropic mean curvature bounded in $L^{p}$ , $p > m$ , are regular almost everywhere in every dimension and codimension. This provi…

math.AP2020

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…

math.AP2019

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…

math.AP2018★ 12 cited

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 $Σ$ in $R^{n + 1}$ and every $p > n$ , the $L^{p}$ -norm of the trace-free part of the anisotropic second fun…

math.AP2017

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,…

math.AP2016

Minimization of anisotropic energies in classes of rectifiable varifolds

Antonio De Rosa

We consider the minimization problem of an anisotropic energy in classes of $d$ -rectifiable varifolds in $R^{n}$ , closed under Lipschitz deformations and encoding a suitable…

math.AP2016★ 3 cited

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…

math.AP2016

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].…

math.AP2015

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…