Einstein Constraints and Ricci Flow / Mathematical Physics Studies (PDF)
A Geometrical Averaging of Initial Data Sets
(Sprache: Englisch)
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...
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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.
Autoren-Porträt von Mauro Carfora, Annalisa Marzuoli
Mauro Carfora is Professor of Mathematical Physics at the University of Pavia, Italy. He is co-author with Annalisa Marzuoli of the Springer Lecture Notes in Physics Quantum Triangulations (LNP 845 and LNP 942), and illustrator of the popular relativity book Flat and Curved Spacetimes by George. F. R. Ellis and Ruth Williams.Annalisa Marzuoli is Associate Professor of Mathematical Physics at the University of Pavia, Italy. She is co-author with Jan Ambjørn and Mauro Carfora of the Springer Lecture Notes in Physics The Geometry of Dynamical Triangulations (Springer LNP m50).
Bibliographische Angaben
- Autoren: Mauro Carfora , Annalisa Marzuoli
- 2023, 1st ed. 2023, 173 Seiten, Englisch
- Verlag: Springer Nature Singapore
- ISBN-10: 9811985405
- ISBN-13: 9789811985409
- Erscheinungsdatum: 10.01.2023
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
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- Dateiformat: PDF
- Größe: 2.97 MB
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Sprache:
Englisch
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