Geometric Flows and the Geometry of Space-time

Geometric Flows and the Geometry of Space-time PDF

Author: Vicente Cortés

Publisher: Springer

Published: 2018-12-05

Total Pages: 121

ISBN-13: 3030011267

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This book consists of two lecture notes on geometric flow equations (O. Schnürer) and Lorentzian geometry - holonomy, spinors and Cauchy Problems (H. Baum and T. Leistner) written by leading experts in these fields. It grew out of the summer school “Geometric flows and the geometry of space-time” held in Hamburg (2016) and provides an excellent introduction for students of mathematics and theoretical physics to important themes of current research in global analysis, differential geometry and mathematical physics

Extrinsic Geometric Flows

Extrinsic Geometric Flows PDF

Author: Bennett Chow

Publisher: American Mathematical Soc.

Published: 2020-05-14

Total Pages: 790

ISBN-13: 147045596X

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Extrinsic geometric flows are characterized by a submanifold evolving in an ambient space with velocity determined by its extrinsic curvature. The goal of this book is to give an extensive introduction to a few of the most prominent extrinsic flows, namely, the curve shortening flow, the mean curvature flow, the Gauß curvature flow, the inverse-mean curvature flow, and fully nonlinear flows of mean curvature and inverse-mean curvature type. The authors highlight techniques and behaviors that frequently arise in the study of these (and other) flows. To illustrate the broad applicability of the techniques developed, they also consider general classes of fully nonlinear curvature flows. The book is written at the level of a graduate student who has had a basic course in differential geometry and has some familiarity with partial differential equations. It is intended also to be useful as a reference for specialists. In general, the authors provide detailed proofs, although for some more specialized results they may only present the main ideas; in such cases, they provide references for complete proofs. A brief survey of additional topics, with extensive references, can be found in the notes and commentary at the end of each chapter.

Spacetime

Spacetime PDF

Author: Marcus Kriele

Publisher: Springer Science & Business Media

Published: 1999-10-19

Total Pages: 444

ISBN-13: 3540663770

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This textbook is for mathematicians and mathematical physicists and is mainly concerned with the physical justification of both the mathematical framework and the foundations of the theory of general relativity. Previous knowledge of the relevant physics is not assumed. This book is also suitable as an introduction to pseudo-Riemannian geometry with emphasis on geometrical concepts. A significant part of the text is devoted to the discussion of causality and singularity theorems. The insights obtained are applied to black hole astrophysics, thereby making the connection to current active research in mathematical physics and cosmology.

Space, Time and Geometry

Space, Time and Geometry PDF

Author: Patrick Suppes

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 437

ISBN-13: 9401026866

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The articles in this volume have been stimulated in two different ways. More than two years ago the editor of Synthese, laakko Hintikka, an nounced a special issue devoted to space and time, and articles were solicited. Part of the reason for that announcement was also the second source of papers. Several years ago I gave a seminar on special relativity at Stanford, and the papers by Domotor, Harrison, Hudgin, Latzer and myself partially arose out of discussion in that seminar. All of the papers except those of Griinbaum, Fine, the second paper of Friedman, and the paper of Adams appeared in a special double issue of Synthese (24 (1972), Nos. 1-2). I am pleased to have been able to add the four additional papers mentioned in making the special issue a volume in the Synthese Library. Of these four additional articles, only the one by Fine has pre viously appeared in print (Synthese 22 (1971), 448-481); its relevance to the present volume is apparent. In preparing the papers for publication and in carrying out the various editonal chores of such a task, I am very much indebted to Mrs. Lillian O'Toole for her extensive assistance. INTRODUCTION The philosophy of space and time has been of permanent importance in philosophy, and most of the major historical figures in philosophy, such as Aristotle, Descartes and Kant, have had a good deal to say about the nature of space and time.

Spacetime, Geometry, Cosmology

Spacetime, Geometry, Cosmology PDF

Author: William L. Burke

Publisher: Courier Dover Publications

Published: 2020-12-16

Total Pages: 353

ISBN-13: 0486845583

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Novel interpretation of the relationship between space, time, gravitation, and their cosmological implications; based on author's discovery of a value in gravitation overlooked by both Newton and Einstein. 1982 edition.

Spacetime and Singularities

Spacetime and Singularities PDF

Author: Gregory L. Naber

Publisher: Cambridge University Press

Published: 1988

Total Pages: 196

ISBN-13: 9780521336123

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An elementary introduction to the geometrical methods and notions used in special and general relativity. Emphasizes the ideas concerned with structure of space-time that play a role in Penrose-Hawking singularity theorems.

Geometric Flows on Planar Lattices

Geometric Flows on Planar Lattices PDF

Author: Andrea Braides

Publisher: Springer Nature

Published: 2021-03-23

Total Pages: 134

ISBN-13: 303069917X

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This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gamma-convergence tools, applications of geometric measure theory, properties of interfacial energies, etc. This is done by tackling a prototypical problem of interfacial evolution in heterogeneous media, where these concepts are introduced and elaborated in a natural and constructive way. At the same time, the analysis introduces open issues of a general and fundamental nature, at the core of important applications. The focus on two-dimensional lattices as a prototype of heterogeneous media allows visual descriptions of concepts and methods through a large amount of illustrations.

Spacetime and Geometry

Spacetime and Geometry PDF

Author: Sean M. Carroll

Publisher: Cambridge University Press

Published: 2019-08-08

Total Pages: 529

ISBN-13: 1108488390

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An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.

Curvature of Space and Time, with an Introduction to Geometric Analysis

Curvature of Space and Time, with an Introduction to Geometric Analysis PDF

Author: Iva Stavrov

Publisher:

Published:

Total Pages: 243

ISBN-13: 9781470463137

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This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations.After addressing concepts in geometry such as metrics, covariant differentiation, tensor calculus and curvature, the book explains the mathematical framework for both special and general relativity. Relativistic concepts discussed include (initial value formulation of) the Einstein equations, stress-ene.