Geometric & Functional Analysis GAFA

, Volume 16, Issue 1, pp 164–229

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

Original Paper

DOI: 10.1007/s00039-006-0557-8

Cite this article as:
Klainerman, S. & Rodnianski, I. GAFA, Geom. funct. anal. (2006) 16: 164. doi:10.1007/s00039-006-0557-8

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.

Keywords and phrases.

Sobolev trace inequalitiesLittlewood–Paley theorynull hypersurfaces

2000 Mathematics Subject Classification.

35J10

Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA