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.

Original languageEnglish (US)
Pages (from-to)164-229
Number of pages66
JournalGeometric and Functional Analysis
Volume16
Issue number1
DOIs
StatePublished - Feb 1 2006

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

Keywords

  • Littlewood-Paley theory
  • Null hypersurfaces
  • Sobolev trace inequalities

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