Reinaldo Resende

activity

20222026

most citedDensity of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity

2 citations · 6 across the 7 of their papers we have counts for

collaborators

9 papers

math.DG2026

The generalized Cartan-Hadamard conjecture

Marcos Agnoletto, Márcio Fabiano Da Silva, Stefano Nardulli +1

We establish the generalized Cartan-Hadamard conjecture, including rigidity in the equality case. As a corollary, we obtain that isoperimetric regions are bounded. We prove the con…

math.DG2026

A proof of the Cartan-Hadamard conjecture for small volumes under a Ricci curvature lower bound

Marcos Agnoletto, Márcio Fabiano Da Silva, Stefano Nardulli +1

We prove the generalized Cartan-Hadamard conjecture, also known as the Aubin conjecture, in the small volume regime under a lower Ricci curvature bound, for any dimension $n \geq 2$ …

math.AP2025

Rigidity of critical points of hydrophobic capillary functionals

Antonio De Rosa, Robin Neumayer, Reinaldo Resende

We prove the rigidity, among sets of finite perimeter, of volume-preserving critical points of the capillary energy in the half space, in the case where the prescribed interior con…

math.AP2024★ 1 cited

On the regularity of area minimizing currents at boundaries with arbitrary multiplicity

Ian Fleschler, Reinaldo Resende

In this paper, we consider an area minimizing integral $m$ -current $T$ within a submanifold $Σ$ of $R^{m + n}$ , taking a boundary $Γ$ with arbitrary multiplicity $Q \in \mat…

math.AP2024

Interior regularity of area minimizing currents within a $C^{2, α}$ -submanifold

Stefano Nardulli, Reinaldo Resende

Given an area-minimizing integral $m$ -current in $Σ$ , we prove that the Hausdorff dimension of the interior singular set of $T$ cannot exceed $m - 2$ , provided that $Σ$ is an embedde…

math.AP2023★ 1 cited

Lipschitz approximation for general almost area minimizing currents

Reinaldo Resende

We prove a Lipschitz approximation with superlinear error terms for integral currents $ω$ -minimizing the area functional, where $ω$ is a modulus of continuity satisfying a Dini con…

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.AP2022★ 2 cited

Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity

Stefano Nardulli, Reinaldo Resende

In the present work, we consider area minimizing currents in the general setting of arbitrary codimension and arbitrary boundary multiplicity. We study the boundary regularity of 2…

math.AP2022★ 1 cited

Multiplicity of solutions to the multiphasic Allen-Cahn-Hilliard system with a small volume constraint on closed parallelizable manifolds

João Henrique Andrade, Jackeline Conrado, Stefano Nardulli +2

We prove the existence of multiple solutions to the Allen--Cahn--Hilliard (ACH) vectorial equation (with two equations) involving a triple-well (triphasic) potential with a small v…