L. Bonorino

activity

20112026

most citedOn the asymptotic Dirichlet problem for a class of mean curvature type partial differential equations

5 citations · 14 across the 11 of their papers we have counts for

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math.DG2026

Invariant solutions for the asymptotic Plateau problem in $H^{3}$

Matheus Pimentel Gomes, Patrícia Kruse Klaser, Jaime Bruck Ripoll +1

In this paper, we present solutions to the asymptotic Plateau problem in the hyperbolic space $H^{3}$ . In this context, we exhibit solutions for curves that are invariant un…

math.DG2023

On the non-parabolicity of $S o l_{3}$

Leonardo Bonorino, Giovanni Nunes, Álvaro Ramos +3

We prove that $S o l_{3}$ , the isometry group of the Minkowski plane, is non parabolic with respect to any left invariant metric.

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.DG2018★ 5 cited

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…

math.DG2016★ 1 cited

On the nature of isolated asymptotic singularities of solutions of a family of quasi-linear elliptic PDE's on a Cartan-Hadamard manifold

Leonardo Prange Bonorino, Jaime Bruck Ripoll

Let $M$ be a Cartan-Hadamard manifold with sectional curvature satisfying $- b^{2} \leq K \leq - a^{2} < 0$ , $b \geq a > 0.$ Denote by $\partial_{\infty} M$ the asymptotic boundary of $M$ and by…

math.DG2014★ 2 cited

Boundedness of Laplacian eigenfunctions on manifolds of infinite volume

Leonardo Bonorino, Patrícia Klaser, Miriam Telichevesky

In a Hadamard manifold $M$ , it is proved that if $u$ is a $λ$ -eigenfunction of the Laplacian that belongs to $L^{p} (M)$ for some $p \geq 2$ , then $u$ is bounded and $\|u\|_{\infty} \l…

math.DG2013★ 1 cited

Existence and nonexistence results for eigenfunctions of the Laplacian in unbounded domains of H^n

Leonardo Bonorino, Patricia Klaser

We investigate, for the Laplacian operator, the existence and nonexistence of eigenfunctions of eigenvalue between zero and the first eigenvalue of the hyperbolic space H^n, for un…