On the long neck principle and width estimates for initial data sets

In this paper, we prove the long neck principle, band width estimates, and width inequalities of the geodesic collar neighborhoods of the boundary in the setting of general initial data sets for the Einstein equations, subject to certain energy conditions corresponding to the lower bounds of scalar...

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 307; no. 3
Main Author Liu, Daoqiang
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2024
Springer Nature B.V
Subjects
Datasets
Einstein equations
Estimates
Lower bounds
Mathematics
Mathematics and Statistics
Riemann manifold
Primary 53C21
53C50
Width estimate
Callias operator
Initial data set
53C27
Long neck principle
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Summary:In this paper, we prove the long neck principle, band width estimates, and width inequalities of the geodesic collar neighborhoods of the boundary in the setting of general initial data sets for the Einstein equations, subject to certain energy conditions corresponding to the lower bounds of scalar curvature on Riemannian manifolds. Our results are established via the spinorial Callias operator approach.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-024-03532-6