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, spin.
Geometric relativity.
9781470450816
Differential equations, Partial.
General relativity (Physics)-- Mathematics.
Geometry, Riemannian.
Differential equations, Partial.
Differential geometry-- Global differential geometry-- Applications to physics.