Mohameden Ould Ahmedou

Prescribing a fourth oder conformal invariant on the standard sphere - Part I: a perturbation result

In this paper we study some fourth order elliptic equation involving the critical Sobolev exponent, related to the prescription of a fourth order conformal invariant on the standard sphere. We use a topological method to prove the existence of at least a solution when the function to be prescribed is close to a constant and a finite dimensional map associated to it has non-zero degree

On a nonlinear fourth-order elliptic equation involving the critical Sobolev exponent

In this paper we use an algebraic topological argument due to Bahri and Coron to show how the topology of the domain influences the existence of positive solutions of the following problem involving the bilaplacian operator with the critical Sobolev exponent Δ2u = un+4/(n-4) in Ω, u > 0 in Ω, u = Δu = 0 on ∂Ω, where (Ω is a bounded domain of Rn (n≥ 5) with a smooth boundary ∂Ω.

Prescribing scalar and boundary mean curvature on the three dimensional half sphere

We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half-three sphere, by deforming conformally its standard metric. Using blow-up analysis techniques and minimax arguments, we prove some existence and compactness results.

Prescribing the Scalar Curvature under Minimal Boundary Conditions on the Half Sphere

Abstract This paper is devoted to the problem of prescribing the scalar curvature under zero boundary conditions. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we prove some existence results on the standard half sphere.

On the Prescribed Scalar and Zero Mean Curvature on 3-Dimensional Manifolds With Umbilic Boundary

Abstract In this paper we consider the existence and the compactness of Riemannian metrics of prescribed mean curvature and zero boundary mean curvature on a three dimensional manifold with umbilic boundary (M, g0). We prove that for three dimensional manifolds with umbilic boundaries, which are not conformally equivalent to the three dimensional standard half sphere, any positive function can be realized as the scalar curvature of a Riemannian metric g conformal to g0 with respect to which the boundary has zero mean curvature. Moreover, all such metrics stay bounded with respect to the C2,α -topology and in the nondegerate case Morse inequalities hold.

Theory of “Critical Points at Infinity” and a Resonant Singular Liouville-Type Equation

Abstract We consider the following Liouville-type equation on domains of ℝ 2

Prescribing a fourth order conformal invariant on the standard sphere, part II : blow up analysis and applications

{\mathbb{R}^{2}}

Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries

under Dirichlet boundary conditions: { - Δ ⁢ u = ϱ ⁢ K ⁢ e u ∫ Ω K ⁢ e u in ⁢ Ω , u = 0 on ⁢ ∂ ⁡ Ω ,

A GEOMETRIC EQUATION WITH CRITICAL NONLINEARITY ON THE BOUNDARY

\left\{\begin{aligned} \displaystyle-\Delta u&\displaystyle=\varrho\frac{Ke^{u% }}{\int_{\Omega}Ke^{u}}&&\displaystyle\text{in }\Omega,\\ \displaystyle u&\displaystyle=0&&\displaystyle\text{on }\partial\Omega,\end{% aligned}\right.

The prescribed boundary mean curvature problem on B4

where ϱ ∈ ℝ