Geometric Measure Theory

Author: Herbert Federer
Editor: Springer
ISBN: 3642620108
File Size: 17,67 MB
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"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 And Real Analysis

Author: Luigi Ambrosio
Editor: Springer
ISBN: 8876425233
File Size: 47,52 MB
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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.

Geometric Measure Theory

Author: Frank Morgan
Editor: Academic Press
ISBN: 0128045272
File Size: 30,64 MB
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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

Geometric Measure Theory And Free Boundary Problems

Author: Guido De Philippis
Editor: Springer
ISBN: 9783030657987
File Size: 28,99 MB
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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.

Partial Differential Equations And Geometric Measure Theory

Author: Alessio Figalli
Editor: Springer
ISBN: 3319740423
File Size: 40,36 MB
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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.

Geometric Integration Theory

Author: Steven G. Krantz
Editor: Springer Science & Business Media
ISBN: 0817646795
File Size: 80,34 MB
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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.

Advanced Basics Of Geometric Measure Theory

Author: Maria Roginskaya
Editor: Lulu.com
ISBN: 1326367439
File Size: 21,35 MB
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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

Author: Summer Institute on Geometric Measure Theory and the Calculus of Variations (1984 Humbol
Editor: American Mathematical Soc.
ISBN: 0821814702
File Size: 75,66 MB
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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.

Seminar On Geometric Measure Theory

Author: R. Hardt
Editor: Birkhäuser
ISBN:
File Size: 39,20 MB
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Geometric Measure Theory

Author: Fanghua Lin
Editor: International Pressof Boston Incorporated
ISBN: 9781571461254
File Size: 22,68 MB
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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

Author: Robert Hardt
Editor:
ISBN:
File Size: 46,11 MB
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Geometric Measure Theory And Minimal Surfaces

Author: E. Bombieri
Editor:
ISBN: 9783642109713
File Size: 42,14 MB
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Geometric Measure Theory And Minimal Surfaces

Author: E. Bombieri
Editor: Springer Science & Business Media
ISBN: 9783642109706
File Size: 24,84 MB
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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

Author: Francesco Maggi
Editor: Cambridge University Press
ISBN: 1107021030
File Size: 31,46 MB
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An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers.

Lectures On Geometric Measure Theory

Author: Leon Simon
Editor:
ISBN: 9780867844290
File Size: 41,76 MB
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Geometric Measure Theory And Free Boundary Problems

Author: Guido De Philippis
Editor: Springer Nature
ISBN: 303065799X
File Size: 75,56 MB
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Geometric Measure Theory An Introduction

Author: Fanghua Lin
Editor:
ISBN: 9781571462084
File Size: 22,97 MB
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Some Applications Of Geometric Measure Theory

Author: Roger Overy (Eric)
Editor:
ISBN:
File Size: 80,57 MB
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New Trends In Applied Harmonic Analysis Volume 2

Author: Akram Aldroubi
Editor: Springer Nature
ISBN: 3030323536
File Size: 32,53 MB
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This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.