Problèmes de Neumann non linéaires sur les variétés riemanniennes

On the Yamabe problem and the scalar curvature problems under boundary conditions

“…It is well known that such a solution is C ∞ provided g, R and h are, see [10]. If u > 0 is a smooth solution of (1) then g = u 4/(n−2) g is a metric, conformally equivalent to g, such that R and h are, respectively, the scalar curvature of (B, g ) and the mean curvature of (S n−1 , g ).…”

Harmonically free group actions and equivariant bifurcation in the Yamabe problem

“…The existence of solution for these problems was proved in the works of Cherrier [9], Escobar [12], [13], [14], Almaraz [1], Han [15], Marques [17], [18] and others.…”

Existence of conformal metrics with prescribed scalar curvature on the four dimensional half sphere

“…Ben Ayed-El Mehdi-Ould Ahmedou [9], [10] gave some topological conditions on K to prescribe the scalar curvature under minimal boundary conditions on half spheres of dimension n ≥ 4. Note that problem (P ) is in some sense related to the well known scalar curvature problem −Δ g u + (n(n − 2)/4)u = Ku (n+2)/(n−2) , u > 0 in S n (3) to which much work has been devoted (see [3,4,7,13,14,[19][20][21] and the references therein). As for (3), there are topological obstructions of Kazdan-Warner type to solve (P ) (see [11]) and so a natural question arises: under which conditions on K, (P ) has a positive solution?…”