| Abstract: |
| In this talk we present existence result for the conformal scalar curvature equation on $S^n$ with $n\geq 3$. Our result is based on the Lyapunov-Schmidt reduction method without perturbation and the construction of the prescribed function (after being projected to $R^n$) with twin pseudo-peaks in the sense that the two close critical points have the same positive value, equal flatness, and exhibit maximal behavior in certain directions. The process relies on a balance between the two main contributions to the reduced functional, one from the critical points and the other from the interaction of the two bubbles. This is a joint work with Professor Man Chun LEUNG. |
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