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Surveys in Geometric Analysis and Relativity

2011 General relativity (Physics).
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Release : 2011
Genre : General relativity (Physics).
Kind : eBook
Book Rating : 305/5 ( reviews)

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Book Synopsis Surveys in Geometric Analysis and Relativity by : Hubert Lewis Bray

Download or read book Surveys in Geometric Analysis and Relativity written by Hubert Lewis Bray. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: Presents twenty-three selected survey articles on central topics of geometric analysis and general relativity, written by prominent experts in the fields. Topics of geometric analysis include the Yamabe problem, mean curvature flow, minimal surfaces, harmonic maps, collapsing of manifolds, and Kähler-Einstein metrics. General relativity topics include the positive mass theorem, the Penrose inequality, scalar curvature and Einstein's constraint equations, and the positive mass theorem for asymptotically hyperbolic manifolds.

Geometric Relativity

2021-12-20 Mathematics
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Release : 2021-12-20
Genre : Mathematics
Kind : eBook
Book Rating : 236/5 ( reviews)

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Book Synopsis Geometric Relativity by : Dan A. Lee

Download or read book Geometric Relativity written by Dan A. Lee. This book was released on 2021-12-20. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in general relativity are essentially geometric in nature, in the sense that they can be understood in terms of Riemannian geometry and partial differential equations. This book is centered around the study of mass in general relativity using the techniques of geometric analysis. Specifically, it provides a comprehensive treatment of the positive mass theorem and closely related results, such as the Penrose inequality, drawing on a variety of tools used in this area of research, including minimal hypersurfaces, conformal geometry, inverse mean curvature flow, conformal flow, spinors and the Dirac operator, marginally outer trapped surfaces, and density theorems. This is the first time these topics have been gathered into a single place and presented with an advanced graduate student audience in mind; several dozen exercises are also included. The main prerequisite for this book is a working understanding of Riemannian geometry and basic knowledge of elliptic linear partial differential equations, with only minimal prior knowledge of physics required. The second part of the book includes a short crash course on general relativity, which provides background for the study of asymptotically flat initial data sets satisfying the dominant energy condition.

Geometric Analysis, Mathematical Relativity, and Nonlinear Partial Differential Equations

2012-09-25 Mathematics
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Release : 2012-09-25
Genre : Mathematics
Kind : eBook
Book Rating : 499/5 ( reviews)

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Book Synopsis Geometric Analysis, Mathematical Relativity, and Nonlinear Partial Differential Equations by : Mohammad Ghomi

Download or read book Geometric Analysis, Mathematical Relativity, and Nonlinear Partial Differential Equations written by Mohammad Ghomi. This book was released on 2012-09-25. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the Southeast Geometry Seminar for the meetings that took place bi-annually between the fall of 2009 and the fall of 2011, at Emory University, Georgia Institute of Technology, University of Alabama Birmingham, and the University of Tennessee. Talks at the seminar are devoted to various aspects of geometric analysis and related fields, in particular, nonlinear partial differential equations, general relativity, and geometric topology. Articles in this volume cover the following topics: a new set of axioms for General Relativity, CR manifolds, the Mane Conjecture, minimal surfaces, maximal measures, pendant drops, the Funk-Radon-Helgason method, ADM-mass and capacity, and extrinsic curvature in metric spaces.

Relativity and Geometry

2014-05-20 Science
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Release : 2014-05-20
Genre : Science
Kind : eBook
Book Rating : 371/5 ( reviews)

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Book Synopsis Relativity and Geometry by : Roberto Torretti

Download or read book Relativity and Geometry written by Roberto Torretti. This book was released on 2014-05-20. Available in PDF, EPUB and Kindle. Book excerpt: Relativity and Geometry aims to elucidate the motivation and significance of the changes in physical geometry brought about by Einstein, in both the first and the second phases of relativity. The book contains seven chapters and a mathematical appendix. The first two chapters review a historical background of relativity. Chapter 3 centers on Einstein's first Relativity paper of 1905. Subsequent chapter presents the Minkowskian formulation of special relativity. Chapters 5 and 6 deal with Einstein's search for general relativity from 1907 to 1915, as well as some aspects and subsequent developments of the theory. The last chapter explores the concept of simultaneity, geometric conventionalism, and a few other questions concerning space time structure, causality, and time.

Geometric Analysis

2016-05-18 Mathematics
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Release : 2016-05-18
Genre : Mathematics
Kind : eBook
Book Rating : 138/5 ( reviews)

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Book Synopsis Geometric Analysis by : Hubert L. Bray

Download or read book Geometric Analysis written by Hubert L. Bray. This book was released on 2016-05-18. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace–Beltrami operators.

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