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The Ambient Metric
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Book Synopsis The Ambient Metric (AM-178) by : Charles Fefferman
Download or read book The Ambient Metric (AM-178) written by Charles Fefferman and published by Princeton University Press. This book was released on 2012 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics. The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambient obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincaré metrics are introduced and shown to be equivalent to the ambient formulation. Self-dual Poincaré metrics in four dimensions are considered as a special case, leading to a formal power series proof of LeBrun's collar neighborhood theorem proved originally using twistor methods. Conformal curvature tensors are introduced and their fundamental properties are established. A jet isomorphism theorem is established for conformal geometry, resulting in a representation of the space of jets of conformal structures at a point in terms of conformal curvature tensors. The book concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature, applying results in parabolic invariant theory.
Book Synopsis The Ambient Metric by : Charles Fefferman
Download or read book The Ambient Metric written by Charles Fefferman and published by Princeton University Press. This book was released on 2011-12-04 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics. The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambient obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincaré metrics are introduced and shown to be equivalent to the ambient formulation. Self-dual Poincaré metrics in four dimensions are considered as a special case, leading to a formal power series proof of LeBrun's collar neighborhood theorem proved originally using twistor methods. Conformal curvature tensors are introduced and their fundamental properties are established. A jet isomorphism theorem is established for conformal geometry, resulting in a representation of the space of jets of conformal structures at a point in terms of conformal curvature tensors. The book concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature, applying results in parabolic invariant theory.
Book Synopsis The Weighted Ambient Metric by : Ayush Khaitan
Download or read book The Weighted Ambient Metric written by Ayush Khaitan and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct the ambient metric for smooth metric measure space (Mn,g,f,m,[mu]) with m ∈ [0, [infinity symbol]]. With this metric, we construct the GJMS operators and renormalized volume coefficients. We write down the explicit ambient metric for Einstein spaces and locally conformally flat spaces. We also study the total functional and its critical points. We show that Einstein metrics are stable critical points of these functionals. Using the ambient metric for manifolds with density, we construct families of fully non-linear analogues of Perelman's F-functional and W-functional, and study their monotonicity under the gradient Ricci flow.
Book Synopsis Motives, Quantum Field Theory, and Pseudodifferential Operators by : Alan L. Carey
Download or read book Motives, Quantum Field Theory, and Pseudodifferential Operators written by Alan L. Carey and published by American Mathematical Soc.. This book was released on 2010 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles related to the conference ``Motives, Quantum Field Theory, and Pseudodifferntial Operators'' held at Boston University in June 2008, with partial support from the Clay Mathematics Institute, Boston University, and the National Science Foundation. There are deep but only partially understood connections between the three conference fields, so this book is intended both to explain the known connections and to offer directions for further research. In keeping with the organization of the conference, this book contains introductory lectures on each of the conference themes and research articles on current topics in these fields. The introductory lectures are suitable for graduate students and new Ph.D.'s in both mathematics and theoretical physics, as well as for senior researchers, since few mathematicians are expert in any two of the conference areas. Among the topics discussed in the introductory lectures are the appearance of multiple zeta values both as periods of motives and in Feynman integral calculations in perturbative QFT, the use of Hopf algebra techniques for renormalization in QFT, and regularized traces of pseudodifferential operators. The motivic interpretation of multiple zeta values points to a fundamental link between motives and QFT, and there are strong parallels between regularized traces and Feynman integral techniques. The research articles cover a range of topics in areas related to the conference themes, including geometric, Hopf algebraic, analytic, motivic and computational aspects of quantum field theory and mirror symmetry. There is no unifying theory of the conference areas at present, so the research articles present the current state of the art pointing towards such a unification.
Book Synopsis Higher Spin Gauge Theories by : Nicolas Boulanger
Download or read book Higher Spin Gauge Theories written by Nicolas Boulanger and published by MDPI. This book was released on 2018-08-09 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Higher Spin Gauge Theories" that was published in Universe
Book Synopsis Symmetries and Overdetermined Systems of Partial Differential Equations by : Michael Eastwood
Download or read book Symmetries and Overdetermined Systems of Partial Differential Equations written by Michael Eastwood and published by Springer Science & Business Media. This book was released on 2009-04-23 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three-week summer program considered the symmetries preserving various natural geometric structures. There are two parts to the proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.
Book Synopsis Introduction to Tensor Analysis and the Calculus of Moving Surfaces by : Pavel Grinfeld
Download or read book Introduction to Tensor Analysis and the Calculus of Moving Surfaces written by Pavel Grinfeld and published by Springer Science & Business Media. This book was released on 2013-09-24 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.
Book Synopsis Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk by : A. Rod Gover
Download or read book Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk written by A. Rod Gover and published by American Mathematical Soc.. This book was released on 2015-04-09 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. They solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions. They also develop a product formula for solving these asymptotic problems in general. The central tools of their approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary. The latter also controls the breaking of conformal invariance in a very strict way by coupling conformally invariant equations to the scale tractor associated with the generalised scale.
Book Synopsis Final Supplemental Environmental Impact Statement: Comments on the draft SEIS by : United States. Department of the Air Force
Download or read book Final Supplemental Environmental Impact Statement: Comments on the draft SEIS written by United States. Department of the Air Force and published by . This book was released on 2000 with total page 898 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Complex Geometry written by G. Komatsu and published by CRC Press. This book was released on 1992-11-19 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the proceedings of an international conference on complex geometry and related topics, held in commemoration of the 50th anniversary of Osaka University, Osaka, Japan. The text focuses on the CR invariants, hyperbolic geometry, Yamabe-type problems, and harmonic maps.
Book Synopsis Experimental Measurements of the Ground Cloud Effluents and Cloud Growth for the May 20, 1975, Titan IIIC Launch at Air Force Eastern Test Range, Florida by : Gerald L. Gregory
Download or read book Experimental Measurements of the Ground Cloud Effluents and Cloud Growth for the May 20, 1975, Titan IIIC Launch at Air Force Eastern Test Range, Florida written by Gerald L. Gregory and published by . This book was released on 1977 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Final Supplemental Environmental Impact Statement: Appendices by : United States. Department of the Air Force
Download or read book Final Supplemental Environmental Impact Statement: Appendices written by United States. Department of the Air Force and published by . This book was released on 2000 with total page 826 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Draft Supplemental Environmental Impact Statement: Chapters 1 through 9 by : United States. Department of the Air Force
Download or read book Draft Supplemental Environmental Impact Statement: Chapters 1 through 9 written by United States. Department of the Air Force and published by . This book was released on 1999 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Code of Federal Regulations written by and published by . This book was released on 2008 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special edition of the Federal Register, containing a codification of documents of general applicability and future effect ... with ancillaries.
Book Synopsis Ricci Flow and the Poincare Conjecture by : John W. Morgan
Download or read book Ricci Flow and the Poincare Conjecture written by John W. Morgan and published by American Mathematical Soc.. This book was released on 2007 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. in 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative. This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjectu The existence of Ricci flow with surgery has application to 3-manifolds far beyond the Poincare Conjecture. It forms the heart of the proof via Ricci flow of Thurston's Geometrization Conjecture. Thurston's Geometrization Conjecture, which classifies all compact 3-manifolds, will be the subject of a follow-up article. The organization of the material in this book differs from that given by Perelman. From the beginning the authors present all analytic and geometric arguments in the context of Ricci flow with surgery. in addition, the fourth part is a much-expanded version of Perelman's third preprint; it gives the first complete and detailed proof of the finite-time extinction theorem. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology. Clay Mathematics Institute Monograph Series The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Book Synopsis The Code of Federal Regulations of the United States of America by :
Download or read book The Code of Federal Regulations of the United States of America written by and published by . This book was released on 2001 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Code of Federal Regulations is the codification of the general and permanent rules published in the Federal Register by the executive departments and agencies of the Federal Government.
Book Synopsis Sobolev Spaces on Metric Measure Spaces by : Juha Heinonen
Download or read book Sobolev Spaces on Metric Measure Spaces written by Juha Heinonen and published by Cambridge University Press. This book was released on 2015-02-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.
