Rectifiable Sets, Densities and Tangent Measures PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Rectifiable Sets, Densities and Tangent Measures PDF full book. Access full book title Rectifiable Sets, Densities and Tangent Measures by Camillo De Lellis. Download full books in PDF and EPUB format.
Author: Camillo De Lellis Publisher: European Mathematical Society ISBN: 9783037190449 Category : Mathematics Languages : en Pages : 140
Book Description
The characterization of rectifiable sets through the existence of densities is a pearl of geometric measure theory. The difficult proof, due to Preiss, relies on many beautiful and deep ideas and novel techniques. Some of them have already proven useful in other contexts, whereas others have not yet been exploited. These notes give a simple and short presentation of the former and provide some perspective of the latter. This text emerged from a course on rectifiability given at the University of Zurich. It is addressed both to researchers and students; the only prerequisite is a solid knowledge in standard measure theory. The first four chapters give an introduction to rectifiable sets and measures in Euclidean spaces, covering classical topics such as the area formula, the theorem of Marstrand and the most elementary rectifiability criterions. The fifth chapter is dedicated to a subtle rectifiability criterion due to Marstrand and generalized by Mattila, and the last three focus on Preiss' result. The aim is to provide a self-contained reference for anyone interested in an overview of this fascinating topic.
Author: Camillo De Lellis Publisher: European Mathematical Society ISBN: 9783037190449 Category : Mathematics Languages : en Pages : 140
Book Description
The characterization of rectifiable sets through the existence of densities is a pearl of geometric measure theory. The difficult proof, due to Preiss, relies on many beautiful and deep ideas and novel techniques. Some of them have already proven useful in other contexts, whereas others have not yet been exploited. These notes give a simple and short presentation of the former and provide some perspective of the latter. This text emerged from a course on rectifiability given at the University of Zurich. It is addressed both to researchers and students; the only prerequisite is a solid knowledge in standard measure theory. The first four chapters give an introduction to rectifiable sets and measures in Euclidean spaces, covering classical topics such as the area formula, the theorem of Marstrand and the most elementary rectifiability criterions. The fifth chapter is dedicated to a subtle rectifiability criterion due to Marstrand and generalized by Mattila, and the last three focus on Preiss' result. The aim is to provide a self-contained reference for anyone interested in an overview of this fascinating topic.
Author: William K. Allard Publisher: American Mathematical Soc. ISBN: 0821814702 Category : Mathematics Languages : en Pages : 482
Book Description
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.
Author: Terence Tao Publisher: American Mathematical Soc. ISBN: 1470466406 Category : Education Languages : en Pages : 206
Book Description
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: Sergey Bobkov Publisher: American Mathematical Soc. ISBN: 1470436507 Category : Education Languages : en Pages : 138
Book Description
This work is devoted to the study of rates of convergence of the empirical measures μn=1n∑nk=1δXk, n≥1, over a sample (Xk)k≥1 of independent identically distributed real-valued random variables towards the common distribution μ in Kantorovich transport distances Wp. The focus is on finite range bounds on the expected Kantorovich distances E(Wp(μn,μ)) or [E(Wpp(μn,μ))]1/p in terms of moments and analytic conditions on the measure μ and its distribution function. The study describes a variety of rates, from the standard one 1n√ to slower rates, and both lower and upper-bounds on E(Wp(μn,μ)) for fixed n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.
Author: Serguei Germanovich Bobkov Publisher: American Mathematical Soc. ISBN: 082183858X Category : Computers Languages : en Pages : 88
Book Description
In these memoirs Bobkov and Zegarlinski describe interesting developments in infinite dimensional analysis that moved it away from experimental science. Here they also describe Poincar -type inequalities, entropy and Orlicz spaces, LSq and Hardy-type inequalities on the line, probability measures satisfying LSq inequalities on the real line, expo
Author: Constantine A. Balanis Publisher: John Wiley & Sons ISBN: 1394180012 Category : Science Languages : en Pages : 1140
Book Description
Balanis’ Advanced Engineering Electromagnetics The latest edition of the foundational guide to advanced electromagnetics Balanis’ third edition of Advanced Engineering Electromagnetics - a global best-seller for over 30 years - covers the advanced knowledge engineers involved in electromagnetics need to know, particularly as the topic relates to the fast-moving, continuously evolving, and rapidly expanding field of wireless communications. The immense interest in wireless communications and the expected increase in wireless communications systems projects (antennas, microwaves and wireless communications) points to an increase in the number of engineers needed to specialize in this field. Highlights of the 3rd Edition include: A new chapter, on Artificial Impedance Surfaces (AIS), contains material on current and advanced EM technologies, including the exciting and fascinating topic of metasurfaces for: Control and broadband RCS reduction using checkerboard designs. Optimization of antenna fundamental parameters, such as: input impedance, directivity, realized gain, amplitude radiation pattern. Leaky-wave antennas using 1-D and 2-D polarization diverse-holographic high impedance metasurfaces for antenna radiation control and optimization. Associated MATLAB programs for the design of checkerboard metasurfaces for RCS reduction, and metasurface printed antennas and holographic L WA for radiation control and optimization. Throughout the book, there are: Additional examples, numerous end-of-chapter problems, and PPT notes. Fifty three MATLAB computer programs for computations, graphical visualizations and animations. Nearly 4,500 multicolor PowerPoint slides are available for self-study or lecture use.
Author: Leandro Pardo Publisher: MDPI ISBN: 3038979368 Category : Social Science Languages : en Pages : 344
Book Description
This book presents new and original research in Statistical Information Theory, based on minimum divergence estimators and test statistics, from a theoretical and applied point of view, for different statistical problems with special emphasis on efficiency and robustness. Divergence statistics, based on maximum likelihood estimators, as well as Wald’s statistics, likelihood ratio statistics and Rao’s score statistics, share several optimum asymptotic properties, but are highly non-robust in cases of model misspecification under the presence of outlying observations. It is well-known that a small deviation from the underlying assumptions on the model can have drastic effect on the performance of these classical tests. Specifically, this book presents a robust version of the classical Wald statistical test, for testing simple and composite null hypotheses for general parametric models, based on minimum divergence estimators.
Author: Steven G. Krantz Publisher: Springer Science & Business Media ISBN: 0817646795 Category : Mathematics Languages : en Pages : 344
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.
Author: Frank Morgan Publisher: Academic Press ISBN: 0080922406 Category : Mathematics Languages : en Pages : 259
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.
Author: Camillo De Lellis
Author: Camillo De Lellis
Author: Pertti Mattila
Author: William K. Allard
Author: Terence Tao
Author: Sergey Bobkov
Author: Serguei Germanovich Bobkov
Author: Constantine A. Balanis
Author: Leandro Pardo
Author: Steven G. Krantz
Author: Frank Morgan