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On a Yamabe Type Problem on Three Dimensional Thin Annulus
Mohamed Ben Ayed, Khalil El Mehdi, Mokhless Hammami +1
We consider a Yamabe type problem on a family of annulus shaped domains of which becomes "thin" as goes to zero. We show that, for any given positive constant ,…
A Riemannian mapping type Theorem in higher dimensions, Part I: the conformally flat case with umbilic boundary
Mohameden Ould Ahmedou
In this paper we prove that every Riemannian metric on a locally conformally flat manifold with umbilic boundary can be conformally deformed to a scalar flat metric having constant…
Prescribing the scalar curvature under minimal boundary conditions on the half sphere
Mohamed Ben Ayed, Khalil El Mehdi, Mohameden Ould Ahmedou
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 poi…
On a geometric equation with critical nonlinearity on the boundary
Veronica Felli, Mohameden Ould Ahmedou
A theorem of Escobar asserts that, on a positive three dimensional smooth compact Riemannian manifold with boundary which is not conformally equivalent to the standard three dimens…
Prescribing a fourth order conformal invariant on the standard sphere, Part II: blow-up analysis and applications
Zindine Djadli, Andrea Malchiodi, Mohameden Ould Ahmedou
In this paper we perform a fine blow-up analysis for a fourth order elliptic equation involving critical Sobolev exponent, related to the prescription of some conformal invariant o…
Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries
Veronica Felli, Mohameden Ould Ahmedou
This paper is devoted to the study of a problem arising from a geometric context, namely the conformal deformation of a Riemannian metric to a scalar flat one having constant mean…