Asymptotically Symmetric Einstein Metrics

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Asymptotically Symmetric Einstein Metrics

Author : Olivier Biquard
Publisher : American Mathematical Soc.
ISBN 13 : 9780821831663
Total Pages : 116 pages
Book Rating : 4.8/5 (316 download)

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Book Synopsis Asymptotically Symmetric Einstein Metrics by : Olivier Biquard

Download or read book Asymptotically Symmetric Einstein Metrics written by Olivier Biquard and published by American Mathematical Soc.. This book was released on 2006 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The correspondence between Einstein metrics and their conformal boundaries has recently been the focus of great interest. This is particularly so in view of the relation with the physical theory of the AdS/CFT correspondence. In this book, this correspondence is seen in the wider context of asymptotically symmetric Einstein metrics, that is Einstein metrics whose curvature is asymptotic to that of a rank one symmetric space. There is an emphasis on the correspondence betweenEinstein metrics and geometric structures on their boundary at infinity: conformal structures, CR structures, and quaternionic contact structures introduced and studied in the book. Two new constructions of such Einstein metrics are given, using two different kinds of techniques: analytic methods toconstruct complete Einstein metrics, with a unified treatment of all rank one symmetric spaces, relying on harmonic analysis; algebraic methods (twistor theory) to construct local solutions of the Einstein equation near the boundary.

AdS/CFT Correspondence

Author : Olivier Biquard
Publisher : European Mathematical Society
ISBN 13 : 9783037190135
Total Pages : 264 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis AdS/CFT Correspondence by : Olivier Biquard

Download or read book AdS/CFT Correspondence written by Olivier Biquard and published by European Mathematical Society. This book was released on 2005 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its discovery in 1997 by Maldacena, AdS/CFT correspondence has become one of the prime subjects of interest in string theory, as well as one of the main meeting points between theoretical physics and mathematics. On the physical side, it provides a duality between a theory of quantum gravity and a field theory. The mathematical counterpart is the relation between Einstein metrics and their conformal boundaries. The correspondence has been intensively studied, and a lot of progress emerged from the confrontation of viewpoints between mathematics and physics. Written by leading experts and directed at research mathematicians and theoretical physicists as well as graduate students, this volume gives an overview of this important area both in theoretical physics and in mathematics. It contains survey articles giving a broad overview of the subject and of the main questions, as well as more specialized articles providing new insight both on the Riemannian side and on the Lorentzian side of the theory.

Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds

Author : John M. Lee
Publisher : American Mathematical Soc.
ISBN 13 : 9780821865866
Total Pages : 102 pages
Book Rating : 4.8/5 (658 download)

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Book Synopsis Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds by : John M. Lee

Download or read book Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds written by John M. Lee and published by American Mathematical Soc.. This book was released on with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this monograph is to give an elementary and self-contained account of the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinities sufficiently close to that of a given asymptotically hyperbolic Einstein metric with nonpositive curvature. The proof is based on an elementary derivation of sharp Fredholm theorems for self-adjoint geometric linear elliptic operators on asymptotically hyperbolic manifolds.

Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds

Author : John M. Lee
Publisher : American Mathematical Soc.
ISBN 13 : 0821839152
Total Pages : 98 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds by : John M. Lee

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 866 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dirichlet Branes and Mirror Symmetry

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821838482
Total Pages : 698 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Dirichlet Branes and Mirror Symmetry by :

Download or read book Dirichlet Branes and Mirror Symmetry written by and published by American Mathematical Soc.. This book was released on 2009 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.

Geometric Complex Analysis

Author : Jisoo Byun
Publisher : Springer
ISBN 13 : 9811316724
Total Pages : 359 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Geometric Complex Analysis by : Jisoo Byun

Download or read book Geometric Complex Analysis written by Jisoo Byun and published by Springer. This book was released on 2018-09-08 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: The KSCV Symposium, the Korean Conference on Several Complex Variables, started in 1997 in an effort to promote the study of complex analysis and geometry. Since then, the conference met semi-regularly for about 10 years and then settled on being held biannually. The sixth and tenth conferences were held in 2002 and 2014 as satellite conferences to the Beijing International Congress of Mathematicians (ICM) and the Seoul ICM, respectively. The purpose of the KSCV Symposium is to organize the research talks of many leading scholars in the world, to provide an opportunity for communication, and to promote new researchers in this field.

Emerging Topics on Differential Equations and Their Applications

Author : Hua Chen
Publisher : World Scientific
ISBN 13 : 981444975X
Total Pages : 319 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Emerging Topics on Differential Equations and Their Applications by : Hua Chen

Download or read book Emerging Topics on Differential Equations and Their Applications written by Hua Chen and published by World Scientific. This book was released on 2012 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the SinoOCoJapan Conference of Young Mathematicians was to provide a forum for presenting and discussing recent trends and developments in differential equations and their applications, as well as to promote scientific exchanges and collaborations among young mathematicians both from China and Japan.The topics discussed in this proceedings include mean curvature flows, KAM theory, N-body problems, flows on Riemannian manifolds, hyperbolic systems, vortices, water waves, and reaction diffusion systems.

Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow

Author : Maxwell Stolarski
Publisher : American Mathematical Society
ISBN 13 : 147046876X
Total Pages : 160 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow by : Maxwell Stolarski

Download or read book Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow written by Maxwell Stolarski and published by American Mathematical Society. This book was released on 2024-04-17 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

An Introduction to Extremal Kahler Metrics

Author : Gábor Székelyhidi
Publisher : American Mathematical Soc.
ISBN 13 : 1470410478
Total Pages : 210 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis An Introduction to Extremal Kahler Metrics by : Gábor Székelyhidi

Download or read book An Introduction to Extremal Kahler Metrics written by Gábor Székelyhidi and published by American Mathematical Soc.. This book was released on 2014-06-19 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kähler geometry. This book gives an introduction to the study of extremal Kähler metrics and in particular to the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry. The book addresses some of the basic ideas on both the analytic and the algebraic sides of this picture. An overview is given of much of the necessary background material, such as basic Kähler geometry, moment maps, and geometric invariant theory. Beyond the basic definitions and properties of extremal metrics, several highlights of the theory are discussed at a level accessible to graduate students: Yau's theorem on the existence of Kähler-Einstein metrics, the Bergman kernel expansion due to Tian, Donaldson's lower bound for the Calabi energy, and Arezzo-Pacard's existence theorem for constant scalar curvature Kähler metrics on blow-ups.

Conformal Methods in General Relativity

Author : Juan A. Valiente Kroon
Publisher : Cambridge University Press
ISBN 13 : 1009291343
Total Pages : 627 pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis Conformal Methods in General Relativity by : Juan A. Valiente Kroon

Download or read book Conformal Methods in General Relativity written by Juan A. Valiente Kroon and published by Cambridge University Press. This book was released on 2023-01-31 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2016 volume, now reissued as OA, shows how conformal methods can be used to study Einstein's theory of gravity.

Proceedings of the 10th Hellenic Relativity Conference on Recent Developments in Gravity

Author : Kostas D. Kokkotas
Publisher : World Scientific
ISBN 13 : 9812383700
Total Pages : 235 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Proceedings of the 10th Hellenic Relativity Conference on Recent Developments in Gravity by : Kostas D. Kokkotas

Download or read book Proceedings of the 10th Hellenic Relativity Conference on Recent Developments in Gravity written by Kostas D. Kokkotas and published by World Scientific. This book was released on 2003 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the 10th Hellenic Relativity Conference on Recent Developments in Gravity, held in Kalithea, Chalkidiki, Greece from May 30 to June 2, 2002.

CMUC

Author :
Publisher :
ISBN 13 :
Total Pages : 656 pages
Book Rating : 4.:/5 (8 download)

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Book Synopsis CMUC by :

Download or read book CMUC written by and published by . This book was released on 2011 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ricci Solitons in Low Dimensions

Author : Bennett Chow
Publisher : American Mathematical Society
ISBN 13 : 147047428X
Total Pages : 358 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Ricci Solitons in Low Dimensions by : Bennett Chow

Download or read book Ricci Solitons in Low Dimensions written by Bennett Chow and published by American Mathematical Society. This book was released on 2023-09-26 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ricci flow is an exciting subject of mathematics with diverse applications in geometry, topology, and other fields. It employs a heat-type equation to smooth an initial Riemannian metric on a manifold. The formation of singularities in the manifold's topology and geometry is a desirable outcome. Upon closer examination, these singularities often reveal intriguing structures known as Ricci solitons. This introductory book focuses on Ricci solitons, shedding light on their role in understanding singularity formation in Ricci flow and formulating surgery-based Ricci flow, which holds potential applications in topology. Notably successful in dimension 3, the book narrows its scope to low dimensions: 2 and 3, where the theory of Ricci solitons is well established. A comprehensive discussion of this theory is provided, while also establishing the groundwork for exploring Ricci solitons in higher dimensions. A particularly exciting area of study involves the potential applications of Ricci flow in comprehending the topology of 4-dimensional smooth manifolds. Geared towards graduate students who have completed a one-semester course on Riemannian geometry, this book serves as an ideal resource for related courses or seminars centered on Ricci solitons.

Developments in Lorentzian Geometry

Author : Alma L. Albujer
Publisher : Springer Nature
ISBN 13 : 3031053796
Total Pages : 323 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Developments in Lorentzian Geometry by : Alma L. Albujer

Download or read book Developments in Lorentzian Geometry written by Alma L. Albujer and published by Springer Nature. This book was released on 2022-10-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume gathers selected, revised papers presented at the X International Meeting on Lorentzian Geometry (GeLoCor 2021), virtually held at the University of Córdoba, Spain, on February 1-5, 2021. It includes surveys describing the state-of-the-art in specific areas, and a selection of the most relevant results presented at the conference. Taken together, the papers offer an invaluable introduction to key topics discussed at the conference and an overview of the main techniques in use today. This volume also gathers extended revisions of key studies in this field. Bringing new results and examples, these unique contributions offer new perspectives to the original problems and, in most cases, extend and reinforce the robustness of previous findings. Hosted every two years since 2001, the International Meeting on Lorentzian Geometry has become one of the main events bringing together the leading experts on Lorentzian geometry. In this volume, the reader will find studies on spatial and null hypersurfaces, low regularity in general relativity, conformal structures, Lorentz-Finsler spacetimes, and more. Given its scope, the book will be of interest to both young and experienced mathematicians and physicists whose research involves general relativity and semi-Riemannian geometry.

Geometric Analysis

Author : Jingyi Chen
Publisher : Springer Nature
ISBN 13 : 3030349535
Total Pages : 616 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Geometric Analysis by : Jingyi Chen

Download or read book Geometric Analysis written by Jingyi Chen and published by Springer Nature. This book was released on 2020-04-10 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and related PDEs. The book is of significant interest for researchers, including advanced Ph.D. students, working in geometric analysis. Readers who have a secondary interest in geometric analysis will benefit from the survey articles. The results included in this book will stimulate further advances in the subjects: geometric analysis, including complex differential geometry, symplectic geometry, PDEs with a geometric origin, and geometry related to topology. Contributions by Claudio Arezzo, Alberto Della Vedova, Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis, Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang, Tobias Holck Colding, William P. Minicozzi II, Panagiotis Dimakis, Richard Melrose, Akito Futaki, Hajime Ono, Jiyuan Han, Jeff A. Viaclovsky, Bruce Kleiner, John Lott, Sławomir Kołodziej, Ngoc Cuong Nguyen, Chi Li, Yuchen Liu, Chenyang Xu, YanYan Li, Luc Nguyen, Bo Wang, Shiguang Ma, Jie Qing, Xiaonan Ma, Sean Timothy Paul, Kyriakos Sergiou, Tristan Rivière, Yanir A. Rubinstein, Natasa Sesum, Jian Song, Jeffrey Streets, Neil S. Trudinger, Yu Yuan, Weiping Zhang, Xiaohua Zhu and Aleksey Zinger.

Kähler Metric and Moduli Spaces

Author : T. Ochiai
Publisher : Academic Press
ISBN 13 : 1483214672
Total Pages : 472 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Kähler Metric and Moduli Spaces by : T. Ochiai

Download or read book Kähler Metric and Moduli Spaces written by T. Ochiai and published by Academic Press. This book was released on 2013-10-22 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kähler Metric and Moduli Spaces, Volume 18-II covers survey notes from the expository lectures given during the seminars in the academic year of 1987 for graduate students and mature mathematicians who were not experts on the topics considered during the sessions about partial differential equations. The book discusses basic facts on Einstein metrics in complex geometry; Einstein-Kähler metrics with positive or non-positive Ricci curvature; Yang-Mills connections; and Einstein-Hermitian metrics. The text then describes the tangent sheaves of minimal varieties; Ricci-Flat Kähler metrics on affine algebraic manifolds; and degenerations of Kähler-Einstein. The moduli of Einstein metrics on a K3 surface and degeneration of Type I and the uniformization of complex surfaces are also considered. Mathematicians and graduate students taking differential and analytic geometry will find the book useful.