Advanced Basics Of Geometric Measure Theory PDF Download
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| Author | : Maria Roginskaya |
| Publisher | : Lulu.com |
| Total Pages | : 106 |
| Release | : 2015 |
| Genre | : Science |
| ISBN | : 1326367439 |
Download Advanced Basics of Geometric Measure Theory Book in PDF, ePub and Kindle
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 | : Frank Morgan |
| Publisher | : Elsevier |
| Total Pages | : 154 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483277801 |
Download Geometric Measure Theory Book in PDF, ePub and Kindle
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 | : Fanghua Lin |
| Publisher | : |
| Total Pages | : 237 |
| Release | : 2002 |
| Genre | : Geometric measure theory |
| ISBN | : 9787030102713 |
Download Geometric Measure Theory Book in PDF, ePub and Kindle
| Author | : Francesco Maggi |
| Publisher | : Cambridge University Press |
| Total Pages | : 475 |
| Release | : 2012-08-09 |
| Genre | : Mathematics |
| ISBN | : 1139560891 |
Download Sets of Finite Perimeter and Geometric Variational Problems Book in PDF, ePub and Kindle
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 | : Leon Simon |
| Publisher | : |
| Total Pages | : 286 |
| Release | : 1984 |
| Genre | : Geometric measure theory |
| ISBN | : 9780867844290 |
Download Lectures on Geometric Measure Theory Book in PDF, ePub and Kindle
| Author | : Herbert Federer |
| Publisher | : Springer |
| Total Pages | : 694 |
| Release | : 2014-11-25 |
| Genre | : Mathematics |
| ISBN | : 3642620108 |
Download Geometric Measure Theory Book in PDF, ePub and Kindle
"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 | : Luigi Ambrosio |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 193 |
| Release | : 2012-02-21 |
| Genre | : Mathematics |
| ISBN | : 8876423869 |
Download Introduction to Measure Theory and Integration Book in PDF, ePub and Kindle
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 | : Steven G. Krantz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 2008-12-15 |
| Genre | : Mathematics |
| ISBN | : 0817646795 |
Download Geometric Integration Theory Book in PDF, ePub and Kindle
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 | : Pertti Mattila |
| Publisher | : Cambridge University Press |
| Total Pages | : 360 |
| Release | : 1999-02-25 |
| Genre | : Mathematics |
| ISBN | : 9780521655958 |
Download Geometry of Sets and Measures in Euclidean Spaces Book in PDF, ePub and Kindle
This book studies the geometric properties of general sets and measures in euclidean space.
| Author | : William K. Allard |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 482 |
| Release | : 1986 |
| Genre | : Mathematics |
| ISBN | : 0821814702 |
Download Geometric Measure Theory and the Calculus of Variations Book in PDF, ePub and Kindle
Includes twenty-six papers that survey a cross section of work in modern geometric measure theory and its applications in the calculus of variations. This title provides an access to the material, including introductions and summaries of many of the authors' much longer works and a section containing 80 open problems in the field.
