Curvature Blow Up In Doubly Warped Product Metrics Evolving By Ricci Flow
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Curvature Blow Up In Doubly Warped Product Metrics Evolving By Ricci Flow
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Author : Maxwell Stolarski
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-17
Curvature Blow Up In Doubly Warped Product Metrics Evolving By Ricci Flow written by Maxwell Stolarski and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-17 with Mathematics categories.
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Variational Problems In Riemannian Geometry
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Author : Paul Baird
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Variational Problems In Riemannian Geometry written by Paul Baird and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book collects invited contributions by specialists in the domain of elliptic partial differential equations and geometric flows. There are introductory survey articles as well as papers presenting the latest research results. Among the topics covered are blow-up theory for second order elliptic equations; bubbling phenomena in the harmonic map heat flow; applications of scans and fractional power integrands; heat flow for the p-energy functional; Ricci flow and evolution by curvature of networks of curves in the plane.
Hamilton S Ricci Flow
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Author : Bennett Chow
language : en
Publisher: American Mathematical Society, Science Press
Release Date : 2023-07-13
Hamilton S Ricci Flow written by Bennett Chow and has been published by American Mathematical Society, Science Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-13 with Mathematics categories.
Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty. The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible. Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions. A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincaré conjecture and Thurston's geometrization conjecture.
Geometrisation Of 3 Manifolds
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Author :
language : en
Publisher: European Mathematical Society
Release Date : 2010
Geometrisation Of 3 Manifolds written by and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Covering spaces (Topology) categories.
The Geometrisation Conjecture was proposed by William Thurston in the mid 1970s in order to classify compact 3-manifolds by means of a canonical decomposition along essential, embedded surfaces into pieces that possess geometric structures. It contains the famous Poincaré Conjecture as a special case. In 2002, Grigory Perelman announced a proof of the Geometrisation Conjecture based on Richard Hamilton’s Ricci flow approach, and presented it in a series of three celebrated arXiv preprints. Since then there has been an ongoing effort to understand Perelman’s work by giving more detailed and accessible presentations of his ideas or alternative arguments for various parts of the proof. This book is a contribution to this endeavour. Its two main innovations are first a simplified version of Perelman’s Ricci flow with surgery, which is called Ricci flow with bubbling-off, and secondly a completely different and original approach to the last step of the proof. In addition, special effort has been made to simplify and streamline the overall structure of the argument, and make the various parts independent of one another. A complete proof of the Geometrisation Conjecture is given, modulo pre-Perelman results on Ricci flow, Perelman’s results on the ℒ-functional and κ-solutions, as well as the Colding–Minicozzi extinction paper. The book can be read by anyone already familiar with these results, or willing to accept them as black boxes. The structure of the proof is presented in a lengthy introduction, which does not require knowledge of geometric analysis. The bulk of the proof is the existence theorem for Ricci flow with bubbling-off, which is treated in parts I and II. Part III deals with the long time behaviour of Ricci flow with bubbling-off. Part IV finishes the proof of the Geometrisation Conjecture.
Geometric Relativity
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Author : Dan A. Lee
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-25
Geometric Relativity written by Dan A. Lee and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-25 with Differential equations, Partial categories.
Many 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 partial differential equations, with only minimal prior knowledge of physics required. The second part of the book includes a short crash course on general relativity, which provides background for the study of asymptotically flat initial data sets satisfying the dominant energy condition.
The Shape Of Inner Space
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Author : Shing-Tung Yau
language : en
Publisher: Hachette UK
Release Date : 2010-09-07
The Shape Of Inner Space written by Shing-Tung Yau and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-07 with Science categories.
String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe. Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau's penetrating thinking on where we've been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.
Physical Foundations Of Cosmology
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Author : Viatcheslav Mukhanov
language : en
Publisher: Cambridge University Press
Release Date : 2005-11-10
Physical Foundations Of Cosmology written by Viatcheslav Mukhanov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-10 with Science categories.
Inflationary cosmology has been developed over the last twenty years to remedy serious shortcomings in the standard hot big bang model of the universe. This textbook, first published in 2005, explains the basis of modern cosmology and shows where the theoretical results come from. The book is divided into two parts; the first deals with the homogeneous and isotropic model of the Universe, the second part discusses how inhomogeneities can explain its structure. Established material such as the inflation and quantum cosmological perturbation are presented in great detail, however the reader is brought to the frontiers of current cosmological research by the discussion of more speculative ideas. An ideal textbook for both advanced students of physics and astrophysics, all of the necessary background material is included in every chapter and no prior knowledge of general relativity and quantum field theory is assumed.
Encyclopedia Of Distances
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Author : Michel Marie Deza
language : en
Publisher: Springer
Release Date : 2014-10-08
Encyclopedia Of Distances written by Michel Marie Deza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-08 with Mathematics categories.
This updated and revised third edition of the leading reference volume on distance metrics includes new items from very active research areas in the use of distances and metrics such as geometry, graph theory, probability theory and analysis. Among the new topics included are, for example, polyhedral metric space, nearness matrix problems, distances between belief assignments, distance-related animal settings, diamond-cutting distances, natural units of length, Heidegger’s de-severance distance, and brain distances. The publication of this volume coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval. Leaving aside the practical questions that arise during the selection of a ‘good’ distance function, this work focuses on providing the research community with an invaluable comprehensive listing of the main available distances. As well as providing standalone introductions and definitions, the encyclopedia facilitates swift cross-referencing with easily navigable bold-faced textual links to core entries. In addition to distances themselves, the authors have collated numerous fascinating curiosities in their Who’s Who of metrics, including distance-related notions and paradigms that enable applied mathematicians in other sectors to deploy research tools that non-specialists justly view as arcane. In expanding access to these techniques, and in many cases enriching the context of distances themselves, this peerless volume is certain to stimulate fresh research.
Lecture Notes On Mean Curvature Flow
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Author : Carlo Mantegazza
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-28
Lecture Notes On Mean Curvature Flow written by Carlo Mantegazza and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-28 with Mathematics categories.
This book is an introduction to the subject of mean curvature flow of hypersurfaces with special emphasis on the analysis of singularities. This flow occurs in the description of the evolution of numerous physical models where the energy is given by the area of the interfaces. These notes provide a detailed discussion of the classical parametric approach (mainly developed by R. Hamilton and G. Huisken). They are well suited for a course at PhD/PostDoc level and can be useful for any researcher interested in a solid introduction to the technical issues of the field. All the proofs are carefully written, often simplified, and contain several comments. Moreover, the author revisited and organized a large amount of material scattered around in literature in the last 25 years.
Dictionary Of Geophysics Astrophysics And Astronomy
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Author : Richard A. Matzner
language : en
Publisher: CRC Press
Release Date : 2018-10-08
Dictionary Of Geophysics Astrophysics And Astronomy written by Richard A. Matzner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-08 with Science categories.
The Dictionary of Geophysics, Astrophysics, and Astronomy provides a lexicon of terminology covering fields such as astronomy, astrophysics, cosmology, relativity, geophysics, meteorology, Newtonian physics, and oceanography. Authors and editors often assume - incorrectly - that readers are familiar with all the terms in professional literature. With over 4,000 definitions and 50 contributing authors, this unique comprehensive dictionary helps scientists to use terminology correctly and to understand papers, articles, and books in which physics-related terms appear.