{"product_id":"geometric-relativity-9781470466237","title":"Geometric Relativity","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMany 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 part\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cem\u003eGeometric Relatively\u003c\/em\u003e 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\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eRiemannian geometry: Scalar curvature\u003c\/li\u003e\n\u003cli\u003eMinimal hypersurfaces\u003c\/li\u003e\n\u003cli\u003eThe Riemannian positive mass theorem\u003c\/li\u003e\n\u003cli\u003eThe Riemannian Penrose inequality\u003c\/li\u003e\n\u003cli\u003eSpin geometry\u003c\/li\u003e\n\u003cli\u003eQuasi-local mass\u003c\/li\u003e\n\u003cli\u003eInitial data sets: Introduction to general relativity\u003c\/li\u003e\n\u003cli\u003eThe spacetime positive mass theorem\u003c\/li\u003e\n\u003cli\u003eDensity theorems for the constraint equations\u003c\/li\u003e\n\u003cli\u003eSome facts about second-order linear elliptic operators\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":50046689083735,"sku":"9781470466237","price":66.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470466237.jpg?v=1740272281","url":"https:\/\/bookcurl.com\/products\/geometric-relativity-9781470466237","provider":"Book Curl","version":"1.0","type":"link"}