A. Aiolfi

activity

20202023

collaborators

6 papers

math.DG2023

The Dirichlet problem for the minimal surface equation on unbounded helicoidal domains of $R^{m}$

Ari Aiolfi, Caroline Assmann, Jaime Ripoll

We consider a helicoidal group $G$ in $R^{n + 1}$ and unbounded $G$ -invariant $C^{2, α}$ -domains $Ω \subset R^{n + 1}$ whose helicoidal projections are exterior domains…

math.DG2021

Equivalences among parabolicity, comparison principle and capacity on complete Riemannian manifolds

A. Aiolfi, L. Bonorino, J. Ripoll +2

In this work we establish new equivalences for the concept of $p$ -parabolic Riemannian manifolds. We define a concept of comparison principle for elliptic PDE's on exterior domains…

math.DG2021

A Moser/Bernstein type theorem in a Lie group with a left invariant metric under a gradient decay condition

Ari Aiolfi, Leonardo Bonorino, Jaime Ripoll +2

We say that a PDE in a Riemannian manifold $M$ is geometric if,whenever $u$ is a solution of the PDE on a domain $Ω$ of $M$ , the composition $u_{ϕ} := u \circ ϕ$ is also solution on…

math.DG2021

On the Size of Minimal Surfaces in $R^{4}$

Ari Aiolfi, Marc Soret, Marina Ville

The Gauss map $g$ of a surface $Σ$ in $R^{4}$ takes its values in the Grassmannian of oriented 2-planes of $R^{4}$ : $G^{+} (2, 4)$ . We give geometric criteria of stabilit…

math.DG2020

On the existence of foliations by solutions to the exterior Dirichlet problem for the minimal surface equation

Ari Aiolfi, Daniel Bustos, Jaime Ripoll

Given an exterior domain $Ω$ with $C^{2, α}$ boundary in $R^{n}$ , $n \geq 3$ , we obtain a $1$ -parameter family $u_{γ} \in C^{\infty} (Ω)$ , $\left\vert γ\right\vert \l…

math.DG2020

CMC Graphs With Planar Boundary in $H^{2} \times R$

Ari J. Aiolfi, Patrícia Klaser

It is known that for $Ω \subset R^{2}$ an unbounded convex domain and $H > 0$ , there exists a graph $G \subset R^{3}$ of constant mean curvature $H$ over $Ω$ with $\p…

The Dirichlet problem for the minimal surface equation on unbounded helicoidal domains of Rm

Equivalences among parabolicity, comparison principle and capacity on complete Riemannian manifolds

A Moser/Bernstein type theorem in a Lie group with a left invariant metric under a gradient decay condition

On the Size of Minimal Surfaces in R4

On the existence of foliations by solutions to the exterior Dirichlet problem for the minimal surface equation

CMC Graphs With Planar Boundary in H2×R

The Dirichlet problem for the minimal surface equation on unbounded helicoidal domains of $R^{m}$

On the Size of Minimal Surfaces in $R^{4}$

CMC Graphs With Planar Boundary in $H^{2} \times R$