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

TY - JOUR

T1 - Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux

AU - Klainerman, S.

AU - Rodnianski, I.

N1 - Funding Information: Keywords and phrases: Sobolev trace inequalities, Littlewood–Paley theory, null hypersurfaces. 2000 Mathematics Subject Classification: 35J10 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.

PY - 2006/2

Y1 - 2006/2

N2 - 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.

AB - 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.

KW - Littlewood-Paley theory

KW - Null hypersurfaces

KW - Sobolev trace inequalities

UR - http://www.scopus.com/inward/record.url?scp=33646475001&partnerID=8YFLogxK

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U2 - 10.1007/s00039-006-0557-8

DO - 10.1007/s00039-006-0557-8

M3 - Article

SN - 1016-443X

VL - 16

SP - 164

EP - 229

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 1

ER -