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Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux

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Abstract.

The main objective of the paper is to prove a geometric version of sharp trace and product estimates on null hypersurfaces with finite curvature flux. These estimates play a crucial role to control the geometry of such null hypersurfaces. The paper is based on an invariant version of the classical Littlewood–Paley theory, in a noncommutative setting, defined via heat flow on surfaces.

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Correspondence to S. Klainerman.

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Received: April 2004 Revision: June 2005 Accepted: July 2005

The first author is partially supported by NSF grant DMS-0070696. The second author is a Clay Prize Fellow and is partially supported by NSF grant DMS-01007791.

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Klainerman, S., Rodnianski, I. Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux. GAFA, Geom. funct. anal. 16, 164–229 (2006). https://doi.org/10.1007/s00039-006-0557-8

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  • DOI: https://doi.org/10.1007/s00039-006-0557-8

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2000 Mathematics Subject Classification.

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