Geometric Flows and the Geometry of Space-time PDF Download

Author: Vicente Cortés
Publisher: Springer
ISBN: 3030011267
Category : Mathematics
Languages : en
Pages : 121

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Book Description
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

Author: Marcus Kriele
Publisher: Springer Science & Business Media
ISBN: 3540483543
Category : Science
Languages : en
Pages : 444

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Book Description
One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-’ We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities". add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one,should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.

Author: Bennett Chow
Publisher: American Mathematical Soc.
ISBN: 147045596X
Category : Education
Languages : en
Pages : 790

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Book Description
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.

Author: Huai-Dong Cao
Publisher:
ISBN:
Category : Geometry, Differential
Languages : en
Pages : 366

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Book Description

Author: Patrick Suppes
Publisher: Springer Science & Business Media
ISBN: 9401026866
Category : Science
Languages : en
Pages : 437

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Book Description
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.

Author: William L. Burke
Publisher: Courier Dover Publications
ISBN: 0486845583
Category : Science
Languages : en
Pages : 353

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Book Description
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.

Author: Gregory L. Naber
Publisher: Cambridge University Press
ISBN: 9780521336123
Category : Mathematics
Languages : en
Pages : 196

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Book Description
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.

Author: Andrea Braides
Publisher: Springer Nature
ISBN: 303069917X
Category : Mathematics
Languages : en
Pages : 134

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Book Description
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.

Author: Hans Reichenbach
Publisher: Courier Corporation
ISBN: 0486138038
Category : Science
Languages : en
Pages : 340

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Book Description
A clear, penetrating exposition of developments in physical science and mathematics brought about by non-Euclidean geometries, including in-depth coverage of the foundations of geometry, theory of time, other topics.

Author: Jochen Brüning
Publisher: de Gruyter
ISBN: 9783110451351
Category : Mathematics
Languages : en
Pages : 0

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Book Description
At the boundary of mathematics and mathematical physics, this monograph explores recent advances in the mathematical foundations of string theory and cosmology. The geometry of matter and the evolution of geometric structures as well as special solu