This chapter presents the full infinite-order formal theory for ambient metric forms, including the freedom at order n/2 in all dimensions and the precise description of the log terms when n ≤ 4 is even. The description of the solutions with freedom at order n/2 and log terms extends and sharpens results of Kichenassamy [K]. Convergence of the formal series determined by singular nonlinear initial value problems of this type has been considered by several authors; these results imply that the formal series converge if the data are real-analytic.
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