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The Ambient Metric (AM-178)$
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Charles Fefferman and C. Robin Graham

Print publication date: 2011

Print ISBN-13: 9780691153131

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691153131.001.0001

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Ambient Metrics

Ambient Metrics

(p.9) Chapter Two Ambient Metrics
The Ambient Metric (AM-178)

Charles Fefferman

C. Robin Graham

Princeton University Press

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.

Keywords:   conformal geometry, ambient metric forms, infinite-order formal theory

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