Blowing up with infinite energy of conformal metrics on Sⁿ

Abstract

Let (Sⁿ,g0) be the standard n-sphere. In this paper, we construct a sequence of conformal metricswith a given R ad their scalar curvature such that the energy of u_j blows up as. We also construct sequence of g_j with the given scalar curvature assuch that u_j has a simultaneous concentraction of a given number of “bubbles” with the same concentraction centers. These examples show us that the blowing up behavior fo u_j might be very complicated when the prescribled scalar curvature is a small perturbation of a positive constant.