We report on recent progress obtained on the construction and control of a parametrix to the homogeneous wave equation , where is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes bounds on the curvature tensor of is a major step towards the proof of the bounded curvature conjecture.
@article{JEDP_2008____A9_0,
author = {Klainerman, Sergiu and Rodnianski, Igor and Szeftel, Jeremie},
title = {Around the bounded $L^2$ curvature conjecture in general relativity},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
year = {2008},
pages = {1-15},
doi = {10.5802/jedp.53},
language = {en},
url = {http://dml.mathdoc.fr/item/JEDP_2008____A9_0}
}
Klainerman, Sergiu; Rodnianski, Igor; Szeftel, Jeremie. Around the bounded $L^2$ curvature conjecture in general relativity. Journées équations aux dérivées partielles, (2008), pp. 1-15. doi : 10.5802/jedp.53. http://gdmltest.u-ga.fr/item/JEDP_2008____A9_0/
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