Introduction To The H Principle

Author : Y. Eliashberg,Nikolai M. Mishachev
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 49,7 Mb
Release : 2002
Category : Differentiable manifolds
ISBN : 9780821832271

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Introduction to the $h$-Principle by Y. Eliashberg,Nikolai M. Mishachev Pdf

The latest volume in the AMS's high-profile GSM series. The book presents a very accessible exposition of a powerful, but difficult to explain method of solving Partial Differentiel Equations. Would make an excellent text for courses on modern methods for solvng Partial Differential Equations. Very readable treatise of an important and remarkable technique. Strong bookstore candidate.

Author : K. Cieliebak,Y. Eliashberg,N. Mishachev
Publisher : American Mathematical Society
Page : 384 pages
File Size : 43,7 Mb
Release : 2024-01-30
Category : Mathematics
ISBN : 9781470476175

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Introduction to the $h$-Principle by K. Cieliebak,Y. Eliashberg,N. Mishachev Pdf

In differential geometry and topology one often deals with systems of partial differential equations as well as partial differential inequalities that have infinitely many solutions whatever boundary conditions are imposed. It was discovered in the 1950s that the solvability of differential relations (i.e., equations and inequalities) of this kind can often be reduced to a problem of a purely homotopy-theoretic nature. One says in this case that the corresponding differential relation satisfies the $h$-principle. Two famous examples of the $h$-principle, the Nash–Kuiper $C^1$-isometric embedding theory in Riemannian geometry and the Smale–Hirsch immersion theory in differential topology, were later transformed by Gromov into powerful general methods for establishing the $h$-principle. The authors cover two main methods for proving the $h$-principle: holonomic approximation and convex integration. The reader will find that, with a few notable exceptions, most instances of the $h$-principle can be treated by the methods considered here. A special emphasis is made on applications to symplectic and contact geometry. The present book is the first broadly accessible exposition of the theory and its applications, making it an excellent text for a graduate course on geometric methods for solving partial differential equations and inequalities. Geometers, topologists, and analysts will also find much value in this very readable exposition of an important and remarkable topic. This second edition of the book is significantly revised and expanded to almost twice of the original size. The most significant addition to the original book is the new part devoted to the method of wrinkling and its applications. Several other chapters (e.g., on multivalued holonomic approximation and foliations) are either added or completely rewritten.

Author : David Spring
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 41,7 Mb
Release : 2010-12-02
Category : Mathematics
ISBN : 9783034800600

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Convex Integration Theory by David Spring Pdf

§1. Historical Remarks Convex Integration theory, ?rst introduced by M. Gromov [17], is one of three general methods in immersion-theoretic topology for solving a broad range of problems in geometry and topology. The other methods are: (i) Removal of Singularities, introduced by M. Gromov and Y. Eliashberg [8]; (ii) the covering homotopy method which, following M. Gromov’s thesis [16], is also referred to as the method of sheaves. The covering homotopy method is due originally to S. Smale [36] who proved a crucial covering homotopy result in order to solve the classi?cation problem for immersions of spheres in Euclidean space. These general methods are not linearly related in the sense that succ- sive methods subsumed the previous methods. Each method has its own distinct foundation, based on an independent geometrical or analytical insight. Con- quently, each method has a range of applications to problems in topology that are best suited to its particular insight. For example, a distinguishing feature of ConvexIntegrationtheoryisthatitappliestosolveclosed relationsinjetspaces, including certain general classes of underdetermined non-linear systems of par- 1 tial di?erential equations. As a case of interest, the Nash-Kuiper C -isometric immersion theorem can be reformulated and proved using Convex Integration theory (cf. Gromov [18]). No such results on closed relations in jet spaces can be proved by means of the other two methods. On the other hand, many classical results in immersion-theoretic topology, such as the classi?cation of immersions, are provable by all three methods.

Author : Hansjšrg Geiges
Publisher : American Mathematical Soc.
Page : 76 pages
File Size : 54,6 Mb
Release : 2003-05-30
Category : Mathematics
ISBN : 0821865013

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H-principles and Flexibility in Geometry by Hansjšrg Geiges Pdf

The notion of homotopy principle or $h$-principle is one of the key concepts in an elegant language developed by Gromov to deal with a host of questions in geometry and topology. Roughly speaking, for a certain differential geometric problem to satisfy the $h$-principle is equivalent to saying that a solution to the problem exists whenever certain obvious topological obstructions vanish. The foundational examples for applications of Gromov's ideas include (i) Hirsch-Smale immersion theory, (ii) Nash-Kuiper $C^1$-isometric immersion theory, (iii) existence of symplectic and contact structures on open manifolds. Gromov has developed several powerful methods that allow one to prove $h$-principles. These notes, based on lectures given in the Graduiertenkolleg of Leipzig University, present two such methods which are strong enough to deal with applications (i) and (iii).

Author : Hansjörg Geiges
Publisher : Unknown
Page : 58 pages
File Size : 47,5 Mb
Release : 2014-09-11
Category : Electronic books
ISBN : 1470403773

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H-Principles and Flexibility in Geometry by Hansjörg Geiges Pdf

Introduction Differential relations and $h$-principles The $h$-principle for open, invariant relations Convex integration theory Bibliography

Author : Sundaram Thangavelu
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681647

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An Introduction to the Uncertainty Principle by Sundaram Thangavelu Pdf

In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". ... The theo pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.

Author : Yuri A. Abramovich,Y. Abramovich,Charalambos D. Aliprantis
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 49,6 Mb
Release : 2002
Category : Operator theory
ISBN : 9780821821473

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Problems in Operator Theory by Yuri A. Abramovich,Y. Abramovich,Charalambos D. Aliprantis Pdf

This book contains complete solutions to the more than six hundred exercises in the authors' book: Invitation to operator theory--foreword.

Author : Steven Dale Cutkosky
Publisher : American Mathematical Soc.
Page : 198 pages
File Size : 41,6 Mb
Release : 2004
Category : Singularities (Mathematics).
ISBN : 9780821835555

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Resolution of Singularities by Steven Dale Cutkosky Pdf

The notion of singularity is basic to mathematics. In algebraic geometry, the resolution of singularities by simple algebraic mappings is truly a fundamental problem. It has a complete solution in characteristic zero and partial solutions in arbitrary characteristic. The resolution of singularities in characteristic zero is a key result used in many subjects besides algebraic geometry, such as differential equations, dynamical systems, number theory, the theory of $\mathcal{D $-modules, topology, and mathematical physics. This book is a rigorous, but instructional, look at resolutions. A simplified proof, based on canonical resolutions, is given for characteristic zero. There are several proofs given for resolution of curves and surfaces in characteristic zero and arbitrary characteristic. Besides explaining the tools needed for understanding resolutions, Cutkosky explains the history and ideas, providing valuable insight and intuition for the novice (or expert). There are many examples and exercises throughout the text. The book is suitable for a second course on an exciting topic in algebraic geometry. A core course on resolutions is contained in Chapters 2 through 6. Additional topics are covered in the final chapters. The prerequisite is a course covering the basic notions of schemes and sheaves.

Author : Julian B. Barbour,Herbert Pfister
Publisher : Springer Science & Business Media
Page : 558 pages
File Size : 44,8 Mb
Release : 1995-08-11
Category : Science
ISBN : 0817638237

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Mach's Principle by Julian B. Barbour,Herbert Pfister Pdf

This volume is a collection of scholarly articles on the Mach Principle, the impact that this theory has had since the end of the 19th century, and its role in helping Einstein formulate the doctrine of general relativity. 20th-century physics is concerned with the concepts of time, space, motion, inertia and gravity. The documentation on all of these makes this book a reference for those who are interested in the history of science and the theory of general relativity

Author : Burak Ozbagci,András Stipsicz
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 43,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662101674

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Surgery on Contact 3-Manifolds and Stein Surfaces by Burak Ozbagci,András Stipsicz Pdf

This book is about an investigation of recent developments in the field of sympletic and contact structures on four- and three-dimensional manifolds from a topologist’s point of view. In it, two main issues are addressed: what kind of sympletic and contact structures we can construct via surgery theory and what kind of sympletic and contact structures are not allowed via gauge theory and the newly invented Heegaard-Floer theory.

Author : John Bland,Kang-Tae Kim,Steven George Krantz
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 43,6 Mb
Release : 2003
Category : Differential geometry
ISBN : 9780821832738

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Explorations in Complex and Riemannian Geometry by John Bland,Kang-Tae Kim,Steven George Krantz Pdf

This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.

Author : Jiun-Haw Lee,I-Chun Cheng,Hong Hua,Shin-Tson Wu
Publisher : John Wiley & Sons
Page : 376 pages
File Size : 42,5 Mb
Release : 2020-06-10
Category : Technology & Engineering
ISBN : 9781119282198

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Introduction to Flat Panel Displays by Jiun-Haw Lee,I-Chun Cheng,Hong Hua,Shin-Tson Wu Pdf

Introduction to Flat Panel Displays describes the fundamental physics and materials of major flat panel display technologies including LED, OLED, LCD, PDP and FED and reflective displays. A reference for graduate students and new entrants to the display industry, the book currently covers the basic science behind each display technology and gives solved problems and homework problems in each chapter to aid self-study. With advancements in this field, there is enough change in the FPD industry to justify a second edition. This book offers the latest information on modern display technology and features new developments in OLED materials including phosphorescent, TTA, and TADF OLEDS, white light OLED and light extraction. It provides key information on blue phase, automotive lighting, quantum-dot enhanced LCDS, device configurations and performance, and LEDs, specifically nitrate-based. Application features include OLED for mobile, TV, light and flexible OLED, and reflective display specifically e-paper technology and low power consumption displays.

Author : H. F. Baker
Publisher : Trieste Publishing
Page : 330 pages
File Size : 50,5 Mb
Release : 2017-10-04
Category : History
ISBN : 0649680049

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Principles of Geometry. Volume VI. Introduction to the Theory of Algebraic Surfaces and Higher Loci by H. F. Baker Pdf

Trieste Publishing has a massive catalogue of classic book titles. Our aim is to provide readers with the highest quality reproductions of fiction and non-fiction literature that has stood the test of time. The many thousands of books in our collection have been sourced from libraries and private collections around the world.The titles that Trieste Publishing has chosen to be part of the collection have been scanned to simulate the original. Our readers see the books the same way that their first readers did decades or a hundred or more years ago. Books from that period are often spoiled by imperfections that did not exist in the original. Imperfections could be in the form of blurred text, photographs, or missing pages. It is highly unlikely that this would occur with one of our books. Our extensive quality control ensures that the readers of Trieste Publishing's books will be delighted with their purchase. Our staff has thoroughly reviewed every page of all the books in the collection, repairing, or if necessary, rejecting titles that are not of the highest quality. This process ensures that the reader of one of Trieste Publishing's titles receives a volume that faithfully reproduces the original, and to the maximum degree possible, gives them the experience of owning the original work.We pride ourselves on not only creating a pathway to an extensive reservoir of books of the finest quality, but also providing value to every one of our readers. Generally, Trieste books are purchased singly - on demand, however they may also be purchased in bulk. Readers interested in bulk purchases are invited to contact us directly to enquire about our tailored bulk rates.

Author : Martin Aigner,Günter M. Ziegler
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 41,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662223437

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Proofs from THE BOOK by Martin Aigner,Günter M. Ziegler Pdf

According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Author : William David Ground
Publisher : Unknown
Page : 394 pages
File Size : 46,5 Mb
Release : 1883
Category : Electronic
ISBN : OXFORD:590444870

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An examination of the structural principles of ... H. Spencer's philosophy by William David Ground Pdf