Selected Papers from the Journal of Differential Geometry 1967-2017, 5 Volume Set

Selected Papers from the Journal of Differential Geometry 1967-2017, 5 Volume Set PDF

Author: Simon Donaldson

Publisher:

Published: 2017-09-30

Total Pages: 694

ISBN-13: 9781571463395

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These papers have been organized into five volumes by subject matter. The first volume deals with topology, the second with algebraic geometry, the third with geometric ideas, the fourth with geometric analysis, and the fifth with geometric flows. These five volumes provide a condensed version of the Journal of Differential Geometry, helping readers to understand the development of the field of geometry over the past fifty years.

Selected Papers from the Journal of Differential Geometry 1967-2017

Selected Papers from the Journal of Differential Geometry 1967-2017 PDF

Author: Richard S. Hamilton

Publisher:

Published: 2017

Total Pages: 504

ISBN-13: 9781571463388

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This volume presents eleven papers dealing with geometric PDEs, geometric flows, and related subject areas. Among the authors and topics are: Richard S. Hamilton on three-manifolds with positive Ricci curvature; Gerhard Huisken on flow by mean curvature of convex surfaces into spheres; L. C. Evans and J. Spruck on motion of level sets by mean curvature; Yun Gang Chen, Yoshikazu Giga and Shun'ichi Goto on uniqueness and existence of viscosity solutions of generalized mean curvature flow equations; and Bing-Long Chen, Siu-Hung Tang and Xi-Ping Zhu on complete classification of compact four-manifolds with positive isotropic curvature. With a preface by Richard Hamilton.

Fundamentals of Differential Geometry

Fundamentals of Differential Geometry PDF

Author: Serge Lang

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 553

ISBN-13: 1461205417

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This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER

From Riemann to Differential Geometry and Relativity

From Riemann to Differential Geometry and Relativity PDF

Author: Lizhen Ji

Publisher: Springer

Published: 2017-10-03

Total Pages: 647

ISBN-13: 3319600397

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This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.

Homotopy, Homology, and Manifolds

Homotopy, Homology, and Manifolds PDF

Author: John Willard Milnor

Publisher: Amer Mathematical Society

Published: 2009

Total Pages: 368

ISBN-13: 9780821844755

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The development of algebraic topology in the 1950's and 1960's was deeply influenced by the work of Milnor. In this collection of papers the reader finds those original papers and some previously unpublished works. The book is divided into four parts: Homotopy Theory, Homology and Cohomology, Manifolds, and Expository Papers. Introductions to each part provide some historical context and subsequent development. Of particular interest are the articles on classifying spaces, the Steenrod algebra, the introductory notes on foliations and the surveys of work on the Poincare conjecture. Together with the previously published volumes I-III of the Collected Works by John Milnor, volume IV provides a rich portion of the most important developments in geometry and topology from those decades. This volume is highly recommended to a broad mathematical audience, and, in particular, to young mathematicians who will certainly benefit from their acquaintance with Milnor's mode of thinking and writing.

Geometrical Methods of Mathematical Physics

Geometrical Methods of Mathematical Physics PDF

Author: Bernard F. Schutz

Publisher: Cambridge University Press

Published: 1980-01-28

Total Pages: 272

ISBN-13: 1107268141

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In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.

A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics

A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics PDF

Author: Antonio Sergio Teixeira Pires

Publisher: Morgan & Claypool Publishers

Published: 2019-03-21

Total Pages: 171

ISBN-13: 1643273744

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In the last years there have been great advances in the applications of topology and differential geometry to problems in condensed matter physics. Concepts drawn from topology and geometry have become essential to the understanding of several phenomena in the area. Physicists have been creative in producing models for actual physical phenomena which realize mathematically exotic concepts and new phases have been discovered in condensed matter in which topology plays a leading role. An important classification paradigm is the concept of topological order, where the state characterizing a system does not break any symmetry, but it defines a topological phase in the sense that certain fundamental properties change only when the system passes through a quantum phase transition. The main purpose of this book is to provide a brief, self-contained introduction to some mathematical ideas and methods from differential geometry and topology, and to show a few applications in condensed matter. It conveys to physicists the basis for many mathematical concepts, avoiding the detailed formality of most textbooks.

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