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

9789811985409 (electronic bk.)
9811985405 (electronic bk.)
9789811985393
9811985391

Singapore : Springer, [2023]

©2023

English

1 online resource (xii, 173 pages) : illustrations (chiefly color).

10.1007/978-981-19-8540-9 doi

QC173.6

530.1101516362

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. .

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed January 23, 2023).

Mathematical physics studies. 2352-3905

Print version: 9789811985393

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