02870nam 2200493 450 991064425600332120230501213722.0981-19-8540-510.1007/978-981-19-8540-9(MiAaPQ)EBC7175626(Au-PeEL)EBL7175626(CKB)25994458500041(DE-He213)978-981-19-8540-9(PPN)267807198(EXLCZ)992599445850004120230501d2023 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierEinstein constraints and Ricci flow a geometrical averaging of initial data sets /Mauro Carfora, Annalisa Marzuoli1st ed. 2023.Singapore :Springer,[2023]©20231 online resource (181 pages)Mathematical Physics Studies,2352-3905Print version: Carfora, Mauro Einstein Constraints and Ricci Flow Singapore : Springer,c2023 9789811985393 Includes bibliographical references and index.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. .Mathematical Physics Studies,2352-3905Ricci flowRicci flow.618Carfora M(Mauro),52579Marzuoli A(Annalisa),MiAaPQMiAaPQMiAaPQBOOK9910644256003321Einstein constraints and Ricci flow3363903UNINA