Books in the Annals of Mathematics Studies series
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Develops and applies a theory of the ambient metric in conformal geometry. This title includes the derivation of the ambient obstruction tensor and an analysis of the cases of conformally flat and conformally Einstein spaces. It concludes with a construction and characterization ...of scalar conformal invariants in terms of ambient curvature.
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Essential mathematical insights into one of the most important and challenging open problems in general relativity-the stability of black holes One of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations. An affirmati...ve answer to this question would provide strong theoretical support for the physical reality of black holes. In this book, Sergiu Klainerman and Jeremie Szeftel take a first important step toward solving the fundamental black hole stability problem in general relativity by establishing the stability of nonrotating black holes-or Schwarzschild spacetimes-under so-called polarized perturbations. This restriction ensures that the final state of evolution is itself a Schwarzschild space. Building on the remarkable advances made in the past fifteen years in establishing quantitative linear stability, Klainerman and Szeftel introduce a series of new ideas to deal with the strongly nonlinear, covariant features of the Einstein equations. Most preeminent among them is the general covariant modulation (GCM) procedure that allows them to determine the center of mass frame and the mass of the final black hole state. Essential reading for mathematicians and physicists alike, this book introduces a rich theoretical framework relevant to situations such as the full setting of the Kerr stability conjecture.
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Offers a comprehensive account of the Gross-Zagier formula on Shimura curves over real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. This title begins with a conceptual formulation of the Gross-Zagier formula in terms of incoher...ent quaternion algebras and incoherent automorphic representations.
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The application by Fadeev and Pavlov of the Lax-Phillips scattering theory to the automorphic wave equation led Professors Lax and Phillips to reexamine this development within the framework of their theory. This volume sets forth the results of that work in the form of new or mo...re straightforward treatments of the spectral theory of the Laplace-Be
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During the summer of 1965, an informal seminar in geometric topology was held at the University of Wisconsin under the direction of Professor Bing. Twenty-five of these lectures are included in this study, among them Professor Bing's lecture describing the recent attacks of Haken... and Poincare on the Poincare conjectures, and sketching a proof of Ha
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Includes fifteen articles which focus on the developments in complex analysis. This work covers a spectrum of research using the methods of partial differential equations as well as differential and algebraic geometry. It covers topics that include invariants of manifolds, the co...mplex Neumann problem, complex dynamics, Ricci flows, and more.
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This monograph describes a method for analyzing the admissable complex representations of the general linear group G = Gl(N,F) of a non-Archimedian local field F in terms of the structure of these representations when they are restricted to certain compact open subgroups of G.
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Written and revised by D. B. A. Epstein.
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Since Poincare's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP mani...folds ensued, including, in 1969, Siebenmann's refutation of the Haupt
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In essence the proceedings of the 1967 meeting in Baton Rouge, the volume offers significant papers in the topology of infinite dimensional linear spaces, fixed point theory in infinite dimensional spaces, infinite dimensional differential topology, and infinite dimensional point...set topology. Later results of the contributors underscore the basic s
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