LEADER 02870nam 2200493 450 001 9910644256003321 005 20230501213722.0 010 $a981-19-8540-5 024 7 $a10.1007/978-981-19-8540-9 035 $a(MiAaPQ)EBC7175626 035 $a(Au-PeEL)EBL7175626 035 $a(CKB)25994458500041 035 $a(DE-He213)978-981-19-8540-9 035 $a(PPN)267807198 035 $a(EXLCZ)9925994458500041 100 $a20230501d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aEinstein constraints and Ricci flow $ea geometrical averaging of initial data sets /$fMauro Carfora, Annalisa Marzuoli 205 $a1st ed. 2023. 210 1$aSingapore :$cSpringer,$d[2023] 210 4$dİ2023 215 $a1 online resource (181 pages) 225 1 $aMathematical Physics Studies,$x2352-3905 311 08$aPrint version: Carfora, Mauro Einstein Constraints and Ricci Flow Singapore : Springer,c2023 9789811985393 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Geometric preliminaries -- Ricci ?ow background -- Ricci ?ow conjugation of initial data sets -- Concluding remarks. 330 $aThis book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold. This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface. The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory. This work is intended for advanced students in mathematical physics and researchers alike. . 410 0$aMathematical Physics Studies,$x2352-3905 606 $aRicci flow 615 0$aRicci flow. 676 $a618 700 $aCarfora$b M$g(Mauro),$052579 702 $aMarzuoli$b A$g(Annalisa), 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910644256003321 996 $aEinstein constraints and Ricci flow$93363903 997 $aUNINA