14 citations · 54 across the 15 of their papers we have counts for
15 papers
Construction of 2-bubbles for the energy critical bi-harmonic Schrödinger equation
Jean-Baptiste Casteras, Ilkka Holopainen, Léonard Monsaingeon
We construct a blowing-up solution for the energy critical focusing biharmonic nonlinear Schrödinger equation in infinite time in dimension . Our solution is radially sym…
Fourth order Schrödinger equation with mixed dispersion on certain Cartan-Hadamard manifolds
Jean-Baptiste Casteras, Ilkka Holopainen
We study the fourth order Schrödinger equation with mixed dispersion on an -dimensional Cartan-Hadamard manifold. At first, we focus on the case of the hyperbolic space. Using t…
Non-parametric mean curvature flow with prescribed contact angle in Riemannian products
Jean-Baptiste Casteras, Esko Heinonen, Ilkka Holopainen +1
Assuming that there exists a translating soliton with speed in a domain and with prescribed contact angle on , we prove that a graphical solution to t…
Translating solitons over Cartan-Hadamard manifolds
Jean-Baptiste Casteras, Esko Heinonen, Ilkka Holopainen +1
We prove existence results for entire graphical translators of the mean curvature flow (the so-called bowl solitons) on Cartan-Hadamard manifolds. We show that the asymptotic behav…
Asymptotic Plateau problem for prescribed mean curvature hypersurfaces
Jean-Baptiste Casteras, Ilkka Holopainen, Jaime B. Ripoll
We prove the existence of solutions to the asymptotic Plateau problem for hypersurfaces of prescribed mean curvature in Cartan-Hadamard manifolds . More precisely, given a suita…
Asymptotic Dirichlet problems in warped products
Jean-Baptiste Casteras, Esko Heinonen, Ilkka Holopainen +1
We study the asymptotic Dirichlet problem for Killing graphs with prescribed mean curvature in warped product manifolds . In the first part of the p…
Existence and non-existence of minimal graphic and -harmonic functions
Jean-Baptiste Casteras, Esko Heinonen, Ilkka Holopainen
We prove that every entire solution of the minimal graph equation that is bounded from below and has at most linear growth must be constant on a complete Riemannian manifold wi…
Dirichlet problem for -minimal graphs
Jean-Baptiste Casteras, Esko Heinonen, Ilkka Holopainen
We study the asymptotic Dirichlet problem for -minimal graphs in Cartan-Hadamard manifolds . -minimal hypersurfaces are natural generalizations of self-shrinkers which pla…
Convexity at infinity in Cartan-Hadamard manifolds and applications to the asymptotic Dirichlet and Plateau problems
Jean-baptiste Casteras, Ilkka Holopainen, Jaime Ripoll
We study the asymptotic Dirichlet and Plateau problems on Cartan-Hadamard manifolds satisfying the so-called Strict Convexity (abbr. SC) condition. The main part of the paper consi…
Solvability of minimal graph equation under pointwise pinching condition for sectional curvatures
Jean-Baptiste Casteras, Esko Heinonen, Ilkka Holopainen
We study the asymptotic Dirichlet problem for the minimal graph equation on a Cartan-Hadamard manifold whose radial sectional curvatures outside a compact set satisfy an upper…
Asymptotic Dirichlet problem for A-harmonic and minimal graph equations in Cartan-Hadamard manifolds
Jean-Baptiste Casteras, Ilkka Holopainen, Jaime B. Ripoll
We study the asymptotic Dirichlet problem for A-harmonic equations and for the minimal graph equation on a Cartan-Hadamard manifold M whose sectional curvatures are bounded from be…
Nonsolvability of the asymptotic Dirichlet problems for some quasilinear elliptic PDEs on Hadamard manifolds
Ilkka Holopainen, Jaime Ripoll
We show, by modifying Borbély's example, that there are -dimen\-sional Cartan-Hadamard manifolds , with sectional curvatures , such that the asymptotic Dirichlet prob…
On the asymptotic Dirichlet problem for the minimal hypersurface equation in a Hadamard manifold
Jean-Baptiste Casteras, Ilkka Holopainen, Jaime B. Ripoll
We study the Dirichlet problem at infinity on a Cartan-Hadamard manifold for a large class of operators containing in particular the p-Laplacian and the minimal graph operator.
Global comparison principles for the -Laplace operator on Riemannian manifolds
Stefano Pigola, Giona Veronelli
We prove global comparison results for the -Laplacian on a -parabolic manifold. These involve both real-valued and vector-valued maps with finite -energy.
p-Capacity and p-hyperbolicity of submanifolds
Ilkka Holopainen, Steen Markvorsen, Vicente Palmer
We use drifted Brownian motion in warped product model spaces as comparison constructions to show -hyperbolicity of a large class of submanifolds for . The condition for…