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Einstein constraints and Ricci flow ...

Carfora, Mauro.

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Einstein constraints and Ricci flow = a geometrical averaging of initial data sets /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Einstein constraints and Ricci flow/ by Mauro Carfora, Annalisa Marzuoli.
Reminder of title:	a geometrical averaging of initial data sets /
Author:	Carfora, Mauro.
other author:	Marzuoli, Annalisa.
Published:	Singapore :Springer Nature Singapore : : 2023.,
Description:	xii, 173 p. :ill. (chiefly color), digital ;24 cm.
[NT 15003449]:	Introduction -- Geometric preliminaries -- Ricci ﬂow background -- Ricci ﬂow conjugation of initial data sets -- Concluding remarks.
Contained By:	Springer Nature eBook
Subject:	General relativity (Physics) - Mathematics. -
Online resource:	https://doi.org/10.1007/978-981-19-8540-9
ISBN:	9789811985409

Einstein constraints and Ricci flow = a geometrical averaging of initial data sets /
Carfora, Mauro.

Einstein constraints and Ricci flowa geometrical averaging of initial data sets /[electronic resource] :by Mauro Carfora, Annalisa Marzuoli. - Singapore :Springer Nature Singapore :2023. - xii, 173 p. :ill. (chiefly color), digital ;24 cm. - Mathematical physics studies,2352-3905. - Mathematical physics studies..

Introduction -- Geometric preliminaries -- Ricci ﬂow background -- Ricci ﬂow conjugation of initial data sets -- Concluding remarks.

This book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold. This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface. The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory. This work is intended for advanced students in mathematical physics and researchers alike.

ISBN: 9789811985409

Standard No.: 10.1007/978-981-19-8540-9doiSubjects--Topical Terms:

906707
General relativity (Physics)
--Mathematics.

LC Class. No.: QC173.6 / .C37 2023

Dewey Class. No.: 530.1101516362

Einstein constraints and Ricci flow = a geometrical averaging of initial data sets /
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505 0 $a Introduction -- Geometric preliminaries -- Ricci ﬂow background -- Ricci ﬂow conjugation of initial data sets -- Concluding remarks.
520 $a This book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold. This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface. The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory. This work is intended for advanced students in mathematical physics and researchers alike.
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