Geometric Analysis On Real Analytic Manifolds

Author : Andrew D. Lewis
Publisher : Springer Nature
ISBN 13 : 3031379136
Total Pages : 323 pages
Book Rating : 4.30/5 ( download)

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Download or read book Geometric Analysis on Real Analytic Manifolds written by Andrew D. Lewis and published by Springer Nature. This book was released on 2023-12-09 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides some useful tools for performing global geometric analysis on real analytic manifolds. At the core of the methodology of the book is a variety of descriptions for the topologies for the space of real analytic sections of a real analytic vector bundle and for the space of real analytic mappings between real analytic manifolds. Among the various descriptions for these topologies is a development of geometric seminorms for the space of real analytic sections. To illustrate the techniques in the book, a number of fundamental constructions in differential geometry are shown to induce continuous mappings on spaces of real analytic sections and mappings. Aimed at researchers at the level of Doctoral students and above, the book introduces the reader to the challenges and opportunities of real analytic analysis and geometry.

Author : Christian Bär
Publisher : Springer Science & Business Media
ISBN 13 : 3642228429
Total Pages : 520 pages
Book Rating : 4.21/5 ( download)

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Download or read book Global Differential Geometry written by Christian Bär and published by Springer Science & Business Media. This book was released on 2011-12-18 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.

Author : R. Narasimhan
Publisher : Elsevier
ISBN 13 : 0080960227
Total Pages : 263 pages
Book Rating : 4.27/5 ( download)

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Download or read book Analysis on Real and Complex Manifolds written by R. Narasimhan and published by Elsevier. This book was released on 1985-12-01 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sard's theorem and Whitney's approximation theorem. The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincaré and Grothendieck with applications of Grothendieck's lemma to complex analysis, the imbedding theorem of Whitney and Thom's transversality theorem. Chapter 3 includes characterizations of linear differentiable operators, due to Peetre and Hormander. The inequalities of Garding and of Friedrichs on elliptic operators are proved and are used to prove the regularity of weak solutions of elliptic equations. The chapter ends with the approximation theorem of Malgrange-Lax and its application to the proof of the Runge theorem on open Riemann surfaces due to Behnke and Stein.

Author : Hubert L. Bray
Publisher : American Mathematical Soc.
ISBN 13 : 1470423138
Total Pages : 456 pages
Book Rating : 4.31/5 ( download)

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Download or read book Geometric Analysis written by Hubert L. Bray and published by American Mathematical Soc.. This book was released on 2016-05-18 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace–Beltrami operators.

Author : KRANTZ
Publisher : Birkhäuser
ISBN 13 : 3034876440
Total Pages : 190 pages
Book Rating : 4.45/5 ( download)

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Download or read book A Primer of Real Analytic Functions written by KRANTZ and published by Birkhäuser. This book was released on 2013-03-09 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of real analytic functions is one of the oldest in mathe matical analysis. Today it is encountered early in ones mathematical training: the first taste usually comes in calculus. While most work ing mathematicians use real analytic functions from time to time in their work, the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible treatment of Puiseux's theorem is in Lefschetz's quite old Algebraic Geometry, that the clearest discussion of resolution of singularities for real analytic manifolds is in a book review by Michael Atiyah, that there is no comprehensive discussion in print of the embedding prob lem for real analytic manifolds. We have had occasion in our collaborative research to become ac quainted with both the history and the scope of the theory of real analytic functions. It seems both appropriate and timely for us to gather together this information in a single volume. The material presented here is of three kinds. The elementary topics, covered in Chapter 1, are presented in great detail. Even results like a real ana lytic inverse function theorem are difficult to find in the literature, and we take pains here to present such topics carefully. Topics of middling difficulty, such as separate real analyticity, Puiseux series, the FBI transform, and related ideas (Chapters 2-4), are covered thoroughly but rather more briskly.

Author : John Bland
Publisher : American Mathematical Soc.
ISBN 13 : 0821832735
Total Pages : 338 pages
Book Rating : 4.38/5 ( download)

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Download or read book Explorations in Complex and Riemannian Geometry written by John Bland and published by American Mathematical Soc.. This book was released on 2003 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Bruno Bianchini
Publisher : Springer Nature
ISBN 13 : 3030627047
Total Pages : 291 pages
Book Rating : 4.41/5 ( download)

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Download or read book Geometric Analysis of Quasilinear Inequalities on Complete Manifolds written by Bruno Bianchini and published by Springer Nature. This book was released on 2021-01-18 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.

Author : Steven George Krantz
Publisher : Birkhauser
ISBN 13 : 9783764327682
Total Pages : 184 pages
Book Rating : 4.85/5 ( download)

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Download or read book A Primer of Real Analytic Functions written by Steven George Krantz and published by Birkhauser. This book was released on 1992-01-01 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treats the subject of analytic functions of one or more real variables, using almost solely the techniques of real analysis, an approach that alters the usual progression of ideas and raises previously neglected questions. The beginning requires only a background in calculus, but the increasingly complex topics require increasing sophistication. Annotation copyright by Book News, Inc., Portland, OR

Author : R. O. Wells
Publisher : Springer Science & Business Media
ISBN 13 : 147573946X
Total Pages : 269 pages
Book Rating : 4.66/5 ( download)

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Download or read book Differential Analysis on Complex Manifolds written by R. O. Wells and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The third edition of this standard reference contains a new appendix by Oscar Garcia-Prada which gives an overview of certain developments in the field during the decades since the book first appeared. From reviews of the 2nd Edition: "..the new edition of Professor Wells' book is timely and welcome...an excellent introduction for any mathematician who suspects that complex manifold techniques may be relevant to his work." - Nigel Hitchin, Bulletin of the London Mathematical Society "Its purpose is to present the basics of analysis and geometry on compact complex manifolds, and is already one of the standard sources for this material." - Daniel M. Burns, Jr., Mathematical Reviews

Author : Chris Miller
Publisher : Springer Science & Business Media
ISBN 13 : 1461440416
Total Pages : 247 pages
Book Rating : 4.13/5 ( download)

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Download or read book Lecture Notes on O-Minimal Structures and Real Analytic Geometry written by Chris Miller and published by Springer Science & Business Media. This book was released on 2012-09-14 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations. ​