Exotic solutions of the conformal scalar curvature equation in ℝn

Abstract

We construct global exotic solutions of the conformal scalar curvature equation $\Delta u+[n(n-2)/4]K{u}^{(n+2)/(n-2)}=0$ in $R^n$, with $K(x)$ approaching $1$ near infinity in order as close to the critical exponent as possible.

Résumé

Nous construisons des solutions globales exotiques de l’équation courbure scalaire conforme $\Delta u+[n(n-2)/4]K{u}^{(n+2)/(n-2)}=0$ dans $R^n$, avec $K(x)\to 1$ quand $|x|\to \infty$.