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Geometric Measure Theory

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Geometric Measure Theory

Geometric Measure Theory Book
Author : Herbert Federer
Publisher : Springer
Release : 2014-11-25
ISBN : 3642620108
Language : En, Es, Fr & De

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Book Description :

"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)

Geometric Measure Theory

Geometric Measure Theory Book
Author : Frank Morgan
Publisher : Academic Press
Release : 2008-09-09
ISBN : 9780080922409
Language : En, Es, Fr & De

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Book Description :

Geometric Measure Theory, Fourth Edition, is an excellent text for introducing ideas from geometric measure theory and the calculus of variations to beginning graduate students and researchers. This updated edition contains abundant illustrations, examples, exercises, and solutions; and the latest results on soap bubble clusters, including a new chapter on Double Bubbles in Spheres, Gauss Space, and Tori. It also includes a new chapter on Manifolds with Density and Perelman's Proof of the Poincaré Conjecture. This text is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Morgan emphasizes geometry over proofs and technicalities providing a fast and efficient insight into many aspects of the subject. New to the 4th edition: * Abundant illustrations, examples, exercises, and solutions. * The latest results on soap bubble clusters, including a new chapter on "Double Bubbles in Spheres, Gauss Space, and Tori." * A new chapter on "Manifolds with Density and Perelman's Proof of the Poincaré Conjecture." * Contributions by undergraduates.

Advanced Basics of Geometric Measure Theory

Advanced Basics of Geometric Measure Theory Book
Author : Maria Roginskaya
Publisher : Lulu.com
Release : 2015-08-08
ISBN : 1326367439
Language : En, Es, Fr & De

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Book Description :

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.

Geometric Measure Theory and the Calculus of Variations

Geometric Measure Theory and the Calculus of Variations Book
Author : Summer Institute on Geometric Measure Theory and the Calculus of Variations (1984 Humbol
Publisher : American Mathematical Soc.
Release : 1986
ISBN : 0821814702
Language : En, Es, Fr & De

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Book Description :

These twenty-six papers survey a cross section of current work in modern geometric measure theory and its applications in the calculus of variations. Presently the field consists of a jumble of new ideas, techniques and intuitive hunches; an exchange of information has been hindered, however, by the characteristic length and complexity of formal research papers in higher-dimensional geometric analysis. This volume provides an easier 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. The papers are aimed at analysts and geometers who may use geometric measure-theoretic techniques, and they require a mathematical sophistication at the level of a second year graduate student. The papers included were presented at the 1984 AMS Summer Research Institute held at Humboldt State University. A major theme of this institute was the introduction and application of multiple-valued function techniques as a basic new tool in geometric analysis, highlighted by Almgren's fundamental paper Deformations and multiple-valued functions. Major new results discussed at the conference included the following: Allard's integrality and regularity theorems for surfaces stationary with respect to general elliptic integrands; Scheffer's first example of a singular solution to the Navier-Stokes equations for a fluid flow with opposing force; and Hutchinson's new definition of the second fundamental form of a general varifold.

Geometric Measure Theory and Real Analysis

Geometric Measure Theory and Real Analysis Book
Author : Luigi Ambrosio
Publisher : Springer
Release : 2015-04-09
ISBN : 8876425233
Language : En, Es, Fr & De

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Book Description :

In 2013, a school on Geometric Measure Theory and Real Analysis, organized by G. Alberti, C. De Lellis and myself, took place at the Centro De Giorgi in Pisa, with lectures by V. Bogachev, R. Monti, E. Spadaro and D. Vittone. The book collects the notes of the courses. The courses provide a deep and up to date insight on challenging mathematical problems and their recent developments: infinite-dimensional analysis, minimal surfaces and isoperimetric problems in the Heisenberg group, regularity of sub-Riemannian geodesics and the regularity theory of minimal currents in any dimension and codimension.

Lectures on Geometric Measure Theory

Lectures on Geometric Measure Theory Book
Author : Leon Simon
Publisher : Unknown
Release : 1984
ISBN : 9780867844290
Language : En, Es, Fr & De

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Book Description :

Download Lectures on Geometric Measure Theory book written by Leon Simon, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Geometric Measure Theory and Minimal Surfaces

Geometric Measure Theory and Minimal Surfaces Book
Author : E. Bombieri
Publisher : Springer Science & Business Media
Release : 2011-06-04
ISBN : 9783642109706
Language : En, Es, Fr & De

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Book Description :

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.

Sets of Finite Perimeter and Geometric Variational Problems

Sets of Finite Perimeter and Geometric Variational Problems Book
Author : Francesco Maggi
Publisher : Cambridge University Press
Release : 2012-08-09
ISBN : 1107021030
Language : En, Es, Fr & De

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Book Description :

An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers.

Geometric Measure Theory

Geometric Measure Theory Book
Author : Fanghua Lin,Xiaoping Yang
Publisher : International Pressof Boston Incorporated
Release : 2002
ISBN : 9781571461254
Language : En, Es, Fr & De

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Book Description :

This work is intended to give a quick overview on the subject of the geometric measure theory with emphases on various basic ideas, techniques and their applications in problems arising in the calculus of variations, geometrical analysis and nonlinear partial differential equations.

Geometric Measure Theory and Free Boundary Problems

Geometric Measure Theory and Free Boundary Problems Book
Author : Guido De Philippis
Publisher : Springer Nature
Release : 2021-04-21
ISBN : 303065799X
Language : En, Es, Fr & De

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Book Description :

Download Geometric Measure Theory and Free Boundary Problems book written by Guido De Philippis, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Seminar on Geometric Measure Theory

Seminar on Geometric Measure Theory Book
Author : R. Hardt,Simon,Leon Simon
Publisher : Birkhäuser
Release : 1986
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Seminar on Geometric Measure Theory book written by R. Hardt,Simon,Leon Simon, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Discrete Methods in Geometric Measure Theory

Discrete Methods in Geometric Measure Theory Book
Author : Harangi Viktor
Publisher : Unknown
Release : 2011
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Discrete Methods in Geometric Measure Theory book written by Harangi Viktor, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Elements of geometric measure theory on sub riemannian groups

Elements of geometric measure theory on sub riemannian groups Book
Author : Valentino Magnani
Publisher : Edizioni della Normale
Release : 2003-10-01
ISBN : 9788876421525
Language : En, Es, Fr & De

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Book Description :

The main purpose of this thesis is to extend methods and results of geometric measure theory to the geometries of sub-riemannian groups. Typical features of sub-riemannian structures historically appeared in several fields of mathematics. Perhaps, the first seeds can be found in the 1909 work by Carathéodory on the second principle of thermodynamics. The Carathéodory theorem can be generalized to distributions of any codimension, whose Lie algebra generates the tangent space at each point. The condition on the distribution is known in Nonholonomic Mechanics, subelliptic PDE's and Optimal Control Theory as total nonholonomicity, Hormander condition, bracket generating condition or Chow condition.

Partial Differential Equations and Geometric Measure Theory

Partial Differential Equations and Geometric Measure Theory Book
Author : Alessio Figalli,Enrico Valdinoci,Ireneo Peral
Publisher : Springer
Release : 2018-05-23
ISBN : 3319740423
Language : En, Es, Fr & De

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Book Description :

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.

Lecture Notes on Geometric Measure Theory

Lecture Notes on Geometric Measure Theory Book
Author : Pertti Mattila
Publisher : Unknown
Release : 1986
ISBN : 9788460044369
Language : En, Es, Fr & De

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Book Description :

Download Lecture Notes on Geometric Measure Theory book written by Pertti Mattila, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Some Applications of Geometric Measure Theory

Some Applications of Geometric Measure Theory Book
Author : Roger Overy (Eric)
Publisher : Unknown
Release : 1973
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Some Applications of Geometric Measure Theory book written by Roger Overy (Eric), available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

An introduction to geometric measure theory

An introduction to geometric measure theory Book
Author : Robert Hardt
Publisher : Unknown
Release : 1979
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download An introduction to geometric measure theory book written by Robert Hardt, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Applications of Geometric Measure Theory to Complex and Quasiconformal Analysis

Applications of Geometric Measure Theory to Complex and Quasiconformal Analysis Book
Author : Tyler Charles Bongers
Publisher : Unknown
Release : 2018
ISBN : 9780355839104
Language : En, Es, Fr & De

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Book Description :

Download Applications of Geometric Measure Theory to Complex and Quasiconformal Analysis book written by Tyler Charles Bongers, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Handbook of Measure Theory

Handbook of Measure Theory Book
Author : E. Pap
Publisher : Elsevier
Release : 2002-10-31
ISBN : 9780080533094
Language : En, Es, Fr & De

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Book Description :

The main goal of this Handbook is to survey measure theory with its many different branches and its relations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications which support the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the various areas they contain many special topics and challenging problems valuable for experts and rich sources of inspiration. Mathematicians from other areas as well as physicists, computer scientists, engineers and econometrists will find useful results and powerful methods for their research. The reader may find in the Handbook many close relations to other mathematical areas: real analysis, probability theory, statistics, ergodic theory, functional analysis, potential theory, topology, set theory, geometry, differential equations, optimization, variational analysis, decision making and others. The Handbook is a rich source of relevant references to articles, books and lecture notes and it contains for the reader's convenience an extensive subject and author index.

Geometric Integration Theory

Geometric Integration Theory Book
Author : Steven G. Krantz,Harold R. Parks
Publisher : Springer Science & Business Media
Release : 2008-12-15
ISBN : 9780817646790
Language : En, Es, Fr & De

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Book Description :

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.