TY - BOOK AU - Szeftel,Jeremie TI - Parametrix for wave equations on a rough background III: space-time regularity of the phase T2 - Asterisque, SN - 9782856298824 U1 - 510=4 23 PY - 2018/// CY - Paris : PB - Societe Mathematique de France, KW - Wave equation KW - Einstein field equations N1 - Includes bibliographical references and index N2 - This book is the third of a sequence of four papers dedicated to the construction and the control of a parametrix to the homogenous wave equation [square]gø=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 ER -