On the global well-posedness of energy-critical Schrödinger equations in curved spaces

A Ionescu, B Pausader, G Staffilani - Analysis & PDE, 2012 - msp.org
In this paper we present a method to study global regularity properties of solutions of large-
data critical Schrödinger equations on certain noncompact Riemannian manifolds. We rely …

[HTML][HTML] Sharp Poincaré–Hardy and Poincaré–Rellich inequalities on the hyperbolic space

E Berchio, D Ganguly, G Grillo - Journal of Functional Analysis, 2017 - Elsevier
We study Hardy-type inequalities associated to the quadratic form of the shifted Laplacian−
Δ HN−(N− 1) 2/4 on the hyperbolic space HN,(N− 1) 2/4 being, as it is well-known, the …

Some constructions for the fractional Laplacian on noncompact manifolds

V Banica, M del Mar González, M Sáez - Revista matemática …, 2015 - ems.press
We give a definition of the fractional Laplacian on some noncompact manifolds, through an
extension problem introduced by Caffarelli–Silvestre. While this definition in the compact …

Semilinear Schrödinger flows on hyperbolic spaces: scattering in H1

AD Ionescu, G Staffilani - Mathematische Annalen, 2009 - Springer
We prove global well-posedness and scattering in H 1 for the defocusing nonlinear
Schrödinger equations\left {(i\partial_t+\Delta_g) u= u| u|^ 2 σ;\u (0)= ϕ,. on the hyperbolic …

Uniform resolvent and Strichartz estimates for Schrödinger equations with critical singularities

JM Bouclet, H Mizutani - Transactions of the American Mathematical …, 2018 - ams.org
This paper deals with global dispersive properties of Schrödinger equations with real-valued
potentials exhibiting critical singularities, where our class of potentials is more general than …

Dispersive estimates for the Schrödinger operator on step-2 stratified Lie groups

H Bahouri, C Fermanian-Kammerer, I Gallagher - Analysis & PDE, 2016 - msp.org
The present paper is dedicated to the proof of dispersive estimates on stratified Lie groups of
step 2 for the linear Schrödinger equation involving a sublaplacian. It turns out that the …

Nonlinear waves on 3D hyperbolic space

J Metcalfe, M Taylor - Transactions of the American Mathematical Society, 2011 - ams.org
In this article, global-in-time dispersive estimates and Strichartz estimates are explored for
the wave equation on three dimensional hyperbolic space. Due to the negative curvature …

Minimal blow-up solutions to the mass-critical inhomogeneous NLS equation

V Banica, R Carles, T Duyckaerts - Communications in Partial …, 2010 - Taylor & Francis
We consider the mass-critical focusing nonlinear Schrödinger equation in the presence of
an external potential, when the nonlinearity is inhomogeneous. We show that if the …

Strichartz estimates on asymptotically hyperbolic manifolds

JM Bouclet - Analysis & PDE, 2011 - msp.org
Strichartz estimates on asymptotically hyperbolic manifolds Page 1 ANALYSIS & PDE
mathematical sciences publishers Volume 4 No. 1 2011 JEAN-MARC BOUCLET …

Schrödinger equations on Damek–Ricci spaces

JP Anker, V Pierfelice, M Vallarino - Communications in Partial …, 2011 - Taylor & Francis
In this paper we consider the Laplace–Beltrami operator Δ on Damek–Ricci spaces and
derive pointwise estimates for the kernel of e τΔ, when τ∈ ℂ* with Re τ≥ 0. When τ∈ i ℝ …