Séminaire d'AnalyseOn the singular \sigma_k-Yamabe problem.
jeudi 03 décembre 2009 11:15 - Tours - Salle 2290 (Bât E2)
We prove the existence of constant positive σk- scalar curvature metrics which are complete and conformal to the standard metric on S^n \ Λ, where Λ ⊂ S^n is a finite number of points with cardinality at lest two, and n, k are positive integers such that 2 ≤ 2k < n. In general this problem is equivalent to solve a singular fully nonlinear second order elliptic equation. For k = 1 (i.e., in the case of the ordinary scalar curvature) the problem reduces to solve a semilinear elliptic equation and it has been studied by several authors (Schoen, Mazzeo-Pacard et al.).