āĻāĻ āĻ-āĻŦā§āĻā§āĻ° āĻŦāĻŋāĻˇā§ā§
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.
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.
Â
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. Sp...
āĻāĻ°āĻ āĻā§āĻāĻā§āĻ¨
āĻ˛ā§āĻāĻ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻā§
Dan A. Lee: CUNY Graduate Center and Queens College, New York, NY
Dan A. Lee: CUNY Graduate Center and Queens College, New York, NY
āĻ-āĻŦā§āĻā§ āĻ°ā§āĻāĻŋāĻ āĻĻāĻŋāĻ¨
āĻāĻĒāĻ¨āĻžāĻ° āĻŽāĻ¤āĻžāĻŽāĻ¤ āĻāĻžāĻ¨āĻžāĻ¨āĨ¤
āĻĒāĻ āĻ¨ āĻ¤āĻĨā§āĻ¯
āĻ¸ā§āĻŽāĻžāĻ°ā§āĻāĻĢā§āĻ¨ āĻāĻŦāĻ āĻā§āĻ¯āĻžāĻŦāĻ˛ā§āĻ
Android āĻāĻŦāĻ iPad/iPhone āĻāĻ° āĻāĻ¨ā§āĻ¯ Google Play āĻŦāĻ āĻ
ā§āĻ¯āĻžāĻĒ āĻāĻ¨āĻ¸ā§āĻāĻ˛ āĻāĻ°ā§āĻ¨āĨ¤ āĻāĻāĻŋ āĻāĻĒāĻ¨āĻžāĻ° āĻ
ā§āĻ¯āĻžāĻāĻžāĻāĻ¨ā§āĻā§āĻ° āĻ¸āĻžāĻĨā§ āĻ
āĻā§āĻŽā§āĻāĻŋāĻ āĻ¸āĻŋāĻā§āĻ āĻšā§ āĻ āĻāĻĒāĻ¨āĻŋ āĻ
āĻ¨āĻ˛āĻžāĻāĻ¨ āĻŦāĻž āĻ
āĻĢāĻ˛āĻžāĻāĻ¨ āĻ¯āĻžāĻ āĻĨāĻžāĻā§āĻ¨ āĻ¨āĻž āĻā§āĻ¨ āĻāĻĒāĻ¨āĻžāĻā§ āĻĒā§āĻ¤ā§ āĻĻā§ā§āĨ¤
āĻ˛ā§āĻ¯āĻžāĻĒāĻāĻĒ āĻ āĻāĻŽā§āĻĒāĻŋāĻāĻāĻžāĻ°
Google Play āĻĨā§āĻā§ āĻā§āĻ¨āĻž āĻ
āĻĄāĻŋāĻāĻŦā§āĻ āĻāĻĒāĻ¨āĻŋ āĻāĻŽā§āĻĒāĻŋāĻāĻāĻžāĻ°ā§āĻ° āĻā§ā§āĻŦ āĻŦā§āĻ°āĻžāĻāĻāĻžāĻ°ā§ āĻļā§āĻ¨āĻ¤ā§ āĻĒāĻžāĻ°ā§āĻ¨āĨ¤
eReader āĻāĻŦāĻ āĻ
āĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯ āĻĄāĻŋāĻāĻžāĻāĻ¸
Kobo eReaders-āĻāĻ° āĻŽāĻ¤ā§ e-ink āĻĄāĻŋāĻāĻžāĻāĻ¸ā§ āĻĒāĻĄāĻŧāĻ¤ā§, āĻāĻĒāĻ¨āĻžāĻā§ āĻāĻāĻāĻŋ āĻĢāĻžāĻāĻ˛ āĻĄāĻžāĻāĻ¨āĻ˛ā§āĻĄ āĻ āĻāĻĒāĻ¨āĻžāĻ° āĻĄāĻŋāĻāĻžāĻāĻ¸ā§ āĻā§āĻ°āĻžāĻ¨ā§āĻ¸āĻĢāĻžāĻ° āĻāĻ°āĻ¤ā§ āĻšāĻŦā§āĨ¤ āĻŦā§āĻ¯āĻŦāĻšāĻžāĻ°āĻāĻžāĻ°ā§āĻ° āĻāĻĻā§āĻĻā§āĻļā§āĻ¯ā§ āĻ¤ā§āĻ°āĻŋ āĻ¸āĻšāĻžā§āĻ¤āĻž āĻā§āĻ¨ā§āĻĻā§āĻ°āĻ¤ā§ āĻĻā§āĻā§āĻž āĻ¨āĻŋāĻ°ā§āĻĻā§āĻļāĻžāĻŦāĻ˛ā§ āĻ
āĻ¨ā§āĻ¸āĻ°āĻŖ āĻāĻ°ā§ āĻ¯ā§āĻ¸āĻŦ eReader-āĻ āĻĢāĻžāĻāĻ˛ āĻĒāĻĄāĻŧāĻž āĻ¯āĻžāĻŦā§ āĻ¸ā§āĻāĻžāĻ¨ā§ āĻā§āĻ°āĻžāĻ¨ā§āĻ¸āĻĢāĻžāĻ° āĻāĻ°ā§āĻ¨āĨ¤
