Serie : Astérisque. Vol 401
Paru le 01/07/2018 | Broché 321 pages
Professionnels
This book is the third of a sequence of four papers dedicated to the construction and the control of a parametrix to the homogeneous wave equation (...) = 0, where g is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes L2 bounds on the curvature tensor R of g is a major step of the proof of the bounded L2 curvature conjecture proposed in 2000 and solved in 2015 by S. Klainerman, I. Rodnianski and the author. On a more general level, this book deals with the control of the eikonal equation on a rough background, and with the derivation of L2 bounds for Fourier integral operators on manifolds with rough phases and symbols, and as such is also of independent interest.
