**Graduate Studies in Mathematics**

Volume: 201;
2019;
361 pp;
Softcover

MSC: Primary 53; 83;

**Print ISBN: 978-1-4704-6623-7
Product Code: GSM/201.S**

List Price: $95.00

AMS Member Price: $76.00

MAA Member Price: $85.50

**Electronic ISBN: 978-1-4704-5405-0
Product Code: GSM/201.E**

List Price: $95.00

AMS Member Price: $76.00

MAA Member Price: $85.50

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#### Supplemental Materials

# Geometric Relativity

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*Dan A. Lee*

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.

#### Readership

Graduate students and researchers interested in nonlinear differential equations and, in particular, in mathematical aspects of general relativity.

#### Reviews & Endorsements

'Geometric Relatively' is refreshing in its narrative approach to this topic. The author is open and honest about the material included and the material excluded in the text, explaining when certain material is omitted or glossed over. Indeed, oftentimes finer technical details will be omitted from a proof for the sake of narrative clarity. Overall, this book is a nice textbook for a graduate student to study from or a great reference for a research mathematician. Anyone who is interested in exploring relativity from a geometry perspective or simply interested purely in geometric analysis can gain something from this text.

-- John Ross, Southwestern University

#### Table of Contents

# Table of Contents

## Geometric Relativity

- Cover Cover11
- Title page iii4
- Preface ix10
- Part 1 . Riemannian geometry 114
- Part 2 . Initial data sets 205218
- Back Cover Back Cover1377