Download Full eBooks in PDF
Geometric Measure Theory Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Geometric Measure Theory book. This book definitely worth reading, it is an incredibly well-written.
Author : Herbert Federer
Publisher : Springer
Page : 694 pages
File Size : 43,7 Mb
Release : 2014-11-25
Category : Mathematics
ISBN : 9783642620102
"This book is a major treatise in mathematics and is essential in the working library of the modern analyst." (Bulletin of the London Mathematical Society)
Author : Frank Morgan
Publisher : Elsevier
Page : 154 pages
File Size : 55,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483277806
Geometric Measure Theory: A Beginner's Guide provides information pertinent to the development of geometric measure theory. This book presents a few fundamental arguments and a superficial discussion of the regularity theory. Organized into 12 chapters, this book begins with an overview of the purpose and fundamental concepts of geometric measure theory. This text then provides the measure-theoretic foundation, including the definition of Hausdorff measure and covering theory. Other chapters consider the m-dimensional surfaces of geometric measure theory called rectifiable sets and introduce the two basic tools of the regularity theory of area-minimizing surfaces. This book discusses as well the fundamental theorem of geometric measure theory, which guarantees solutions to a wide class of variational problems in general dimensions. The final chapter deals with the basic methods of geometry and analysis in a generality that embraces manifold applications. This book is a valuable resource for graduate students, mathematicians, and research workers.
Author : Steven G. Krantz,Harold R. Parks
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 46,9 Mb
Release : 2008-12-15
Category : Mathematics
ISBN : 9780817646790
This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.
Author : Leon Simon
Publisher : Unknown
Page : 286 pages
File Size : 44,9 Mb
Release : 1984
Category : Geometric measure theory
ISBN : 0867844299
Author : Francesco Maggi
Publisher : Cambridge University Press
Page : 475 pages
File Size : 44,6 Mb
Release : 2012-08-09
Category : Mathematics
ISBN : 9781139560894
The marriage of analytic power to geometric intuition drives many of today's mathematical advances, yet books that build the connection from an elementary level remain scarce. This engaging introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory to some of the most celebrated results in modern analysis. The theory of sets of finite perimeter provides a simple and effective framework. Topics covered include existence, regularity, analysis of singularities, characterization and symmetry results for minimizers in geometric variational problems, starting from the basics about Hausdorff measures in Euclidean spaces and ending with complete proofs of the regularity of area-minimizing hypersurfaces up to singular sets of codimension 8. Explanatory pictures, detailed proofs, exercises and remarks providing heuristic motivation and summarizing difficult arguments make this graduate-level textbook suitable for self-study and also a useful reference for researchers. Readers require only undergraduate analysis and basic measure theory.
Author : Guido De Philippis,Xavier Ros-Oton,Georg S. Weiss
Publisher : Springer Nature
Page : 138 pages
File Size : 42,5 Mb
Release : 2021-03-23
Category : Mathematics
ISBN : 9783030657994
This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school “Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems” which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro. Providing a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves as well as regularity theory for the obstacle problems and the developments leading to applications to the Stefan problem, this volume will be of interest to students and researchers in mathematical analysis and its applications.
Author : Alessio Figalli,Enrico Valdinoci,Ireneo Peral
Publisher : Springer
Page : 216 pages
File Size : 47,6 Mb
Release : 2018-05-23
Category : Mathematics
ISBN : 9783319740423
This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.
Author : Frank Morgan
Publisher : Academic Press
Page : 272 pages
File Size : 46,6 Mb
Release : 2016-05-02
Category : Mathematics
ISBN : 9780128045275
Geometric Measure Theory: A Beginner's Guide, Fifth Edition provides the framework readers need to understand the structure of a crystal, a soap bubble cluster, or a universe. The book is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Brevity, clarity, and scope make this classic book an excellent introduction to more complex ideas from geometric measure theory and the calculus of variations for beginning graduate students and researchers. Morgan emphasizes geometry over proofs and technicalities, providing a fast and efficient insight into many aspects of the subject, with new coverage to this edition including topical coverage of the Log Convex Density Conjecture, a major new theorem at the center of an area of mathematics that has exploded since its appearance in Perelman's proof of the Poincaré conjecture, and new topical coverage of manifolds taking into account all recent research advances in theory and applications. Focuses on core geometry rather than proofs, paving the way to fast and efficient insight into an extremely complex topic in geometric structures Enables further study of more advanced topics and texts Demonstrates in the simplest possible way how to relate concepts of geometric analysis by way of algebraic or topological techniques Contains full topical coverage of The Log-Convex Density Conjecture Comprehensively updated throughout
Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 206 pages
File Size : 55,5 Mb
Release : 2021-09-03
Category : Education
ISBN : 9781470466404
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Author : Luigi Ambrosio,Giuseppe Da Prato,Andrea Mennucci
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 46,6 Mb
Release : 2012-02-21
Category : Mathematics
ISBN : 9788876423864
This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 2000-2011. The goal of the course was to present, in a quick but rigorous way, the modern point of view on measure theory and integration, putting Lebesgue's Euclidean space theory into a more general context and presenting the basic applications to Fourier series, calculus and real analysis. The text can also pave the way to more advanced courses in probability, stochastic processes or geometric measure theory. Prerequisites for the book are a basic knowledge of calculus in one and several variables, metric spaces and linear algebra. All results presented here, as well as their proofs, are classical. The authors claim some originality only in the presentation and in the choice of the exercises. Detailed solutions to the exercises are provided in the final part of the book.
Author : Fanghua Lin,Xiaoping Yang
Publisher : Unknown
Page : 237 pages
File Size : 46,9 Mb
Release : 2010
Category : Geometric measure theory
ISBN : 1571462082
Author : Pertti Mattila
Publisher : Cambridge University Press
Page : 360 pages
File Size : 49,7 Mb
Release : 1999-02-25
Category : Mathematics
ISBN : 0521655951
This book studies the geometric properties of general sets and measures in euclidean space.
Author : Maria Roginskaya
Publisher : Lulu.com
Page : 106 pages
File Size : 41,6 Mb
Release : 2015
Category : Science
ISBN : 9781326367435
This book is based on lecture notes for a short course for Masters level or senior undergraduate students. It may also serve as easy (and hopefully pleasant) reading for researchers in a different field of Mathematics. The main purpose of the book is to look closely at some results that are basic for modern Analysis and which fascinated the author when she was a student, and to show how they constitute a foundation for the branch of Analysis known as Geometric Measure Theory. The secondary aim of the book is to give a straightforward but reasonably complete introduction to the definition of Hausdorff measure and Hausdorff dimension and to illustrate how non-trivial they can be. The course has no ambition to replace a serious course on Geometric Measure Theory, but rather to encourage the student to take such a course. The author comes from Russia. For the past 17 years she has worked at Chalmers University of Technology in Gothenburg, Sweden. She also had visiting positions in Canada, France, and Poland.
Author : E. Bombieri
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 53,6 Mb
Release : 2011-06-04
Category : Mathematics
ISBN : 9783642109706
W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems.- E. GIUSTI: Minimal surfaces with obstacles.- J. GUCKENHEIMER: Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities.- M. MIRANDA: Boundaries of Caciopoli sets in the calculus of variations.- L. PICCININI: De Giorgi’s measure and thin obstacles.
Author : Jan Rataj,Martina Zähle
Publisher : Springer
Page : 256 pages
File Size : 48,6 Mb
Release : 2019-06-22
Category : Mathematics
ISBN : 9783030181833
The book describes how curvature measures can be introduced for certain classes of sets with singularities in Euclidean spaces. Its focus lies on sets with positive reach and some extensions, which include the classical polyconvex sets and piecewise smooth submanifolds as special cases. The measures under consideration form a complete system of certain Euclidean invariants. Techniques of geometric measure theory, in particular, rectifiable currents are applied, and some important integral-geometric formulas are derived. Moreover, an approach to curvatures for a class of fractals is presented, which uses approximation by the rescaled curvature measures of small neighborhoods. The book collects results published during the last few decades in a nearly comprehensive way.
