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Categorical Perspectives

Posted By: AvaxGenius
Date: 1 Feb 2024 05:56:35
Categorical Perspectives

Categorical Perspectives by Jürgen Koslowski, Austin Melton
English | PDF | 2001 | 285 Pages | ISBN : 0817641866 | 23.1 MB

"Categorical Perspectives" consists of introductory surveys as well as articles containing original research and complete proofs devoted mainly to the theoretical and foundational developments of category theory and its applications to other fields. A number of articles in the areas of topology, algebra and computer science reflect the varied interests of George Strecker to whom this work is dedicated. Notable also are an exposition of the contributions and importance of George Strecker's research and a survey chapter on general category theory. This work is an excellent reference text for researchers and graduate students in category theory and related areas.
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Microlocal Methods in Mathematical Physics and Global Analysis (Repost)

Posted By: AvaxGenius
Date: 28 Jan 2024 05:16:07
Microlocal Methods in Mathematical Physics and Global Analysis (Repost)

Microlocal Methods in Mathematical Physics and Global Analysis by Daniel Grieser, Stefan Teufel, Andras Vasy
English | PDF (True) | 2013 | 147 Pages | ISBN : 3034804652 | 1.5 MB

Microlocal analysis is a field of mathematics that was invented in the mid-20th century for the detailed investigation of problems from partial differential equations, which incorporated and made rigorous many ideas that originated in physics. Since then it has grown to a powerful machine which is used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. In this book extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held at the University of Tübingen from the 14th to the 18th of June 2011, are collected.​
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Positivity (Repost)

Posted By: AvaxGenius
Date: 28 Jan 2024 03:47:39
Positivity (Repost)

Positivity by Karim Boulabiar, Gerard Buskes, Abdelmajid Triki
English | PDF (True) | 2007 | 282 Pages | ISBN : 3764384778 | 2.5 MB

This book presents nine survey articles addressing topics surrounding positivity, with an emphasis on functional analysis. The book assembles a wide spectrum of research into positivity, providing up-to-date information on topics of current interest. The discussion provides insight into classical areas like spaces of continuous functions, f-algebras, and integral operators. The coverage extends is broad, including vector measures, operator spaces, ordered tensor products, and non-commutative Banach function spaces.
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Classical Tessellations and Three-Manifolds

Posted By: AvaxGenius
Date: 27 Jan 2024 22:44:53
Classical Tessellations and Three-Manifolds

Classical Tessellations and Three-Manifolds by José María Montesinos-Amilibia
English | PDF | 1987 | 248 Pages | ISBN : 3540152911 | 13.7 MB

This unusual book, richly illustrated with 29 colour illustrations and about 200 line drawings, explores the relationship between classical tessellations and three-manifolds. In his original and entertaining style, the author provides graduate students with a source of geometrical insight into low-dimensional topology. Researchers in this field will find here an account of a theory that is on the one hand known to them but here is "clothed in a different garb" and can be used as a source for seminars on low-dimensional topology, or for preparing independent study projects for students, or again as the basis of a reading course.
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Einstein Manifolds

Posted By: AvaxGenius
Date: 26 Jan 2024 18:17:04
Einstein Manifolds

Einstein Manifolds by Arthur L. Besse
English | PDF | 1987 | 523 Pages | ISBN : 3540741208 | 45.9 MB

Einstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. Recently, it has produced several striking results, which have been of great interest also to physicists. This Ergebnisse volume is the first book which presents an up-to-date overview of the state of the art in this field. "Einstein Manifold"s is a successful attempt to organize the abundant literature, with emphasis on examples. Parts of it can be used separately as introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals.
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Variational Inequalities and Frictional Contact Problems

Posted By: AvaxGenius
Date: 19 Jan 2024 17:55:06
Variational Inequalities and Frictional Contact Problems

Variational Inequalities and Frictional Contact Problems by Anca Capatina
English | PDF (True) | 2014 | 242 Pages | ISBN : 3319101625 | 2.1 MB

Variational Inequalities and Frictional Contact Problems contains a carefully selected collection of results on elliptic and evolutionary quasi-variational inequalities including existence, uniqueness, regularity, dual formulations, numerical approximations and error estimates ones. By using a wide range of methods and arguments, the results are presented in a constructive way, with clarity and well justified proofs. This approach makes the subjects accessible to mathematicians and applied mathematicians. Moreover, this part of the book can be used as an excellent background for the investigation of more general classes of variational inequalities. The abstract variational inequalities considered in this book cover the variational formulations of many static and quasi-static contact problems. Based on these abstract results, in the last part of the book, certain static and quasi-static frictional contact problems in elasticity are studied in an almost exhaustive way.
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Smooth Manifolds and Observables

Posted By: AvaxGenius
Date: 9 Jan 2024 22:35:45
Smooth Manifolds and Observables

Smooth Manifolds and Observables by Jet Nestruev
English | PDF (True) | 2003 | 226 Pages | ISBN : 0387955437 | 3.3 MB

This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.
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Introduction to Differentiable Manifolds

Posted By: AvaxGenius
Date: 11 Dec 2023 17:20:40
Introduction to Differentiable Manifolds

Introduction to Differentiable Manifolds by Serge Lang
English | PDF (True) | 2002 | 258 Pages | ISBN : 0387954775 | 2.9 MB

This book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. A certain number of concepts are essential for all three of these areas, and are so basic and elementary, that it is worthwhile to collect them together so that more advanced expositions can be given without having to start from the very beginning. The concepts are concerned with the general basic theory of differential manifolds. As a result, this book can be viewed as a prerequisite to Fundamentals of Differential Geometry. Since this book is intended as a text to follow advanced calculus, manifolds are assumed finite dimensional. In the new edition of this book, the author has made numerous corrections to the text and he has added a chapter on applications of Stokes' Theorem.
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The Volume of Vector Fields on Riemannian Manifolds: Main Results and Open Problems

Posted By: AvaxGenius
Date: 2 Aug 2023 00:21:32
The Volume of Vector Fields on Riemannian Manifolds: Main Results and Open Problems

The Volume of Vector Fields on Riemannian Manifolds: Main Results and Open Problems by Olga Gil-Medrano
English | PDF EPUB (True) | 2023 | 131 Pages | ISBN : 3031368568 | 11.5 MB

This book focuses on the study of the volume of vector fields on Riemannian manifolds. Providing a thorough overview of research on vector fields defining minimal submanifolds, and on the existence and characterization of volume minimizers, it includes proofs of the most significant results obtained since the subject’s introduction in 1986. Aiming to inspire further research, it also highlights a selection of intriguing open problems, and exhibits some previously unpublished results. The presentation is direct and deviates substantially from the usual approaches found in the literature, requiring a significant revision of definitions, statements, and proofs.
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Torus Actions on Symplectic Manifolds

Posted By: AvaxGenius
Date: 25 Jul 2023 12:34:46
Torus Actions on Symplectic Manifolds

Torus Actions on Symplectic Manifolds by Michèle Audin
English | PDF | 2004 | 331 Pages | ISBN : 3764321768 | 24.1 MB

How I have (re-)written this book The book the reader has in hand was supposed to be a new edition of [14]. I have hesitated quite a long time before deciding to do the re-writing work-the first edition has been sold out for a few years. There was absolutely no question of just correcting numerous misprints and a few mathematical errors. When I wrote the first edition, in 1989, the convexity and Duistermaat-Heckman theorems together with the irruption of toric varieties on the scene of symplectic geometry, due to Delzant, around which the book was organized, were still rather recent (less than ten years). I myself was rather happy with a small contribution I had made to the subject. I was giving a post-graduate course on all that and, well, these were lecture notes, just lecture notes. By chance, the book turned out to be rather popular: during the years since then, I had the opportunity to meet quite a few people(1) who kindly pretended to have learnt the subject in this book. However, the older book does not satisfy at all the idea I have now of what a good book should be. So that this "new edition" is, indeed, another book.
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Natural Operations in Differential Geometry

Posted By: AvaxGenius
Date: 24 Mar 2023 04:25:52
Natural Operations in Differential Geometry

Natural Operations in Differential Geometry by Ivan Kolář , Jan Slovák , Peter W. Michor
English | PDF | 1993 | 440 Pages | ISBN : 3540562354 | 41.94 MB

The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op­ erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M.
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Some Nonlinear Problems in Riemannian Geometry

Posted By: AvaxGenius
Date: 22 Mar 2023 18:20:46
Some Nonlinear Problems in Riemannian Geometry

Some Nonlinear Problems in Riemannian Geometry by Thierry Aubin
English | PDF (True) | 1998 | 414 Pages | ISBN : 3540607528 | 33.23 MB

During the last few years, the field of nonlinear problems has undergone great development. This book consisting of the updated Grundlehren volume 252 by the author and of a newly written part, deals with some important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved. Each problem is explained, up-to-date results are given and proofs are presented. Thus, the reader is given access, for each specific problem, to its present status of solution as well as to the most up-to-date methods for approaching it. The main objective of the book is to explain some methods and new techniques, and to apply them. It deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber.
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Differential Analysis on Complex Manifolds

Posted By: AvaxGenius
Date: 27 Jan 2023 17:14:59
Differential Analysis on Complex Manifolds

Differential Analysis on Complex Manifolds by Raymond O. Wells
English | PDF | 2008 | 315 Pages | ISBN : 0387738916 | 1.9 MB

In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge *-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems.
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Hardy Spaces and Potential Theory on C1 Domains in Riemannian Manifolds

Posted By: roxul
Date: 29 Dec 2022 15:37:04
Hardy Spaces and Potential Theory on C1 Domains in Riemannian Manifolds

Martin Dindos, "Hardy Spaces and Potential Theory on C1 Domains in Riemannian Manifolds "
English | ISBN: 0821840436 | 2007 | 78 pages | PDF | 9 MB
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Geometric Structures on Manifolds

Posted By: arundhati
Date: 29 Dec 2022 15:14:01
Geometric Structures on Manifolds

William M. Goldman, "Geometric Structures on Manifolds"
English | ISBN: 1470471035 | 2023 | 437 pages | PDF | 7 MB
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