9 papers · 1 filter
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 -parabolic Riemannian manifolds. We define a concept of comparison principle for elliptic PDE's on exterior domains…
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 is geometric if,whenever is a solution of the PDE on a domain of , the composition is also solution on…
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 with boundary in , , we obtain a -parameter family , $\left\vert γ\right\vert \l…
Asymptotic and exterior Dirichlet problems for the minimal surface equation in the Heisenberg group with a balanced metric
Fidelis Bittencourt, Edson S. Figueiredo, Pedro Fusieger +1
It is proved that the Heisenberg group with a balanced metric, the sum of the left and right invariant metrics, splits as a Riemannian product $\…
On the asymptotic Dirichlet problem for a class of mean curvature type partial differential equations
Leonardo Prange Bonorino, Jean-Baptiste Casteras, Patricia Kruse Klaser +2
We study the Dirichlet problem for the following prescribed mean curvature PDE $$ \begin{cases} -\operatorname{div}\dfrac{\nabla v}{\sqrt{1+|\nabla v|^{2}}}=f(x,v) \text{ in }Ω\\ v…
Minimal isoparametric submanifolds of and octonionic eigenmaps
Fidelis Bittencourt, Daniel Bustos, Edson Figueiredo +2
We use the octonionic multiplication of to associate, to each unit normal section of a submanifold of an octonionic Gauss map $γ_…