Einstein Constraints and Ricci Flow: A Geometrical Averaging of Initial Data Sets
Jan 2023 · Springer Nature
Ebook
173
Pages
reportRatings and reviews aren’t verified Learn More
About this ebook
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.
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.
About the author
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).
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).
Rate this ebook
Tell us what you think.
Reading information
Smartphones and tablets
Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.
Laptops and computers
You can listen to audiobooks purchased on Google Play using your computer's web browser.
eReaders and other devices
To read on e-ink devices like Kobo eReaders, you'll need to download a file and transfer it to your device. Follow the detailed Help Center instructions to transfer the files to supported eReaders.
