or curvature. The values γ and δ are fixed small constants which come up as specific
parameters in our parametrix construction and in choice of various Lebesgue indices
close to certain “critical” thresholds. In practice these can be computed explicitly,
and in dimension n = 6 values like γ = 1/1000 and δ = 1/100 should do.
Acknowledgements. First and foremost, we would like to thank our advisors
Sergiu Klainerman and Matei Machedon for their continuing support and encour-
agement. This subject matter and our point of view on it owes much to them. We
would also like to thank Igor Rodnianski, Terry Tao, and Daniel Tataru for many
interesting and helpful conversations. This work began at the Institute for Ad-
vanced Study during the Fall 2003 semester when both authors were in attendance.
The second author would like to thank Harvard University for its hospitality during
the Spring of 2004 and Winter 2005.
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