Title: Refined estimates for simple blow-ups of the scalar curvature equation on S^n,
Abstract: In their work on a sharp compactness theorem for the Yamabe problem, Khuri,
Marques and Schoen apply a refined blow-up analysis (what we call `second order
blow-up argument' in this article) to obtain highly accurate approximate
solutions for the Yamabe equation. As for the conformal scalar curvature
equation on S^n with n > 3, we examine the second order blow-up argument and
obtain refined estimate for a blow-up sequence near a simple blow-up point. The
estimate involves local effect from the Taylor expansion of the scalar
curvature function, global effect from other blow-up points, and the balance
formula as expressed in the Pohozaev identity in an essential way.