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"The book will appeal to graduate students and researchers in mathematics and mathematical physics interested in the connections between geometric analysis and general relativity. It builds a bridge from foundational coursework to more specialized results in the field for graduate students beginning their study of the Einstein constraints equations"-- Provided by publisher.
List of contents
Preface; Notation and conventions; 1. Special relativity and Minkowski spacetime; 2. The Einstein equation; 3. Basics of Lorentzian causality; 4. The Penrose singularity theorem; 5. The Einstein constraint equations; 6. Scalar curvature deformation and the Einstein constraint equations; Excursus: first and second variation of area; 7. Asymptotically flat solutions of the Einstein constraint equations; 8. On the center of mass and constant mean curvature surfaces of asymptotically flat initial data sets; 9. On the Riemannian Penrose inequality; References; Index.
About the author
Justin Corvino is Marshall R. Metzgar Professor in the Department of Mathematics at Lafayette College, Pennsylvania. He earned his Ph.D. at Stanford in 2000 under the direction of Richard M. Schoen after completing his undergraduate degree at the Massachusetts Institute of Technology (MIT). He was previously an NSF Postdoctoral Research Fellow and Tamarkin Assistant Professor at Brown University. He spent the fall of 2008 at the Mittag-Leffler Institute in Sweden as a Fulbright Fellow. He has authored or co-authored numerous journal articles in geometric analysis and mathematical physics.Pengzi Miao is a professor in the Department of Mathematics at the University of Miami. He was previously a lecturer at Monash University in Melbourne, Australia. He obtained his Ph.D. from Stanford in 2003 with advisor Richard M. Schoen, after which he worked as a postdoctoral fellow at the Mathematical Sciences Research Institute in Berkeley, California in 2004, and as a Visiting Assistant Professor at UC Santa Barbara from 2004 to 2006. He has authored or co-authored dozens of research articles in geometric analysis and general relativity.
