Sets Of Finite Perimeter And Geometric Variational Problems PDF Download
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Author | : Francesco Maggi |
Publisher | : |
Total Pages | : 475 |
Release | : 2014-05-14 |
Genre | : Geometric measure theory |
ISBN | : 9781139549738 |
Download Sets of Finite Perimeter and Geometric Variational Problems Book in PDF, ePub and Kindle
An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers.
Author | : Francesco Maggi |
Publisher | : Cambridge University Press |
Total Pages | : 475 |
Release | : 2012-08-09 |
Genre | : Mathematics |
ISBN | : 1107021030 |
Download Sets of Finite Perimeter and Geometric Variational Problems Book in PDF, ePub and Kindle
An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers.
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 | : Ke Liang Xiao |
Publisher | : |
Total Pages | : 0 |
Release | : 2022 |
Genre | : |
ISBN | : |
Download An Introduction to Functions of Bounded Variation, Sets of Finite Perimeter and Some Applications to Geometric Variational Problems Book in PDF, ePub and Kindle
"In this thesis, we explore how the theory of functions of bounded variation (BV) establishes an appropriate and versatile framework in the study of geometric variational problems. We begin with a presentation of some fundamental results on BV functions that will allow us to link them to Radon measures. In the special case of characteristic functions with bounded variation, we present structural results on sets of finite perimeter, including a generalization of the Gauss-Green Theorem. This machinery will allow us to assign a notion of perimeter to any set of finite Lebesgue measure, hence allowing non- smooth competitors to be considered in minimization problems involving the surface area. We will then address Plateau's problem and the first variation of the area functional. Finally, we will present the ideas of Steiner symmetrization to provide a proof of the Isoperimetric inequality"--
Author | : Marc Pegon |
Publisher | : |
Total Pages | : 0 |
Release | : 2019 |
Genre | : |
ISBN | : |
Download Some Contributions to Geometric Variational Problems Involving Nonlocal Energies Book in PDF, ePub and Kindle
This thesis is dedicated to the study of two separate geometric variational problems involving nonlocal energies: firstly, the geometry and singularities of fractional harmonic maps,and secondly, an iso perimetric problem with a repulsive integrable potential inspired by Gamow's liquid drop model for the atomic nucleus. On the first topic, we improve already-known results for minimizing 1/2-harmonic maps when the target manifold is a sphere by reducing the upperbound on the Haudorff dimension of the singular set, i.e., the set of points of discontinuity. Wealso characterize so-called minimizing 1/2-harmonic tangent maps from the plane into the unit circle S1, shedding light on the behavior of minimizing 1/2-harmonic maps from R2into S1 near singularities. Finally, when s ∈ (0, 1), we prove partial regularity results for s-harmonic maps into spheres in the stationary and minimizing case, obtaining sharp estimates on the Hausdorffd imension of the set of singularities, depending on the value of s. As for the second topic of the thesis, we study a minimization problem on sets of finite perimeter under a volume constraint, where the functional is the sum of a cohesive perimeter term and a repulsive term given by a general integrable symmetric kernel on Rn. We show that under reasonable assumptions on the behavior near the origin and on some of the moments of this kernel - which include physically relevant Bessel potentials - the problem admits large mass (or volume) minimizers. In addition,after normalization, those minimizers converge to the unit ball as the mass goes to infinity. By studying the stability of the ball, we show that without these assumptions, symmetry breaking can occur, that is, there are cases when the problem admits minimizers which cannot be the ball.
Author | : Andrea Braides |
Publisher | : Springer Nature |
Total Pages | : 134 |
Release | : 2021-03-23 |
Genre | : Mathematics |
ISBN | : 303069917X |
Download Geometric Flows on Planar Lattices Book in PDF, ePub and Kindle
This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gamma-convergence tools, applications of geometric measure theory, properties of interfacial energies, etc. This is done by tackling a prototypical problem of interfacial evolution in heterogeneous media, where these concepts are introduced and elaborated in a natural and constructive way. At the same time, the analysis introduces open issues of a general and fundamental nature, at the core of important applications. The focus on two-dimensional lattices as a prototype of heterogeneous media allows visual descriptions of concepts and methods through a large amount of illustrations.
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 | : 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 | : Andrea Braides |
Publisher | : Springer |
Total Pages | : 184 |
Release | : 2014-07-08 |
Genre | : Mathematics |
ISBN | : 3319019821 |
Download Local Minimization, Variational Evolution and Γ-Convergence Book in PDF, ePub and Kindle
This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.
Author | : Abderrahim Elmoataz |
Publisher | : Springer Nature |
Total Pages | : 584 |
Release | : 2021-04-29 |
Genre | : Computers |
ISBN | : 3030755495 |
Download Scale Space and Variational Methods in Computer Vision Book in PDF, ePub and Kindle
This book constitutes the proceedings of the 8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021, which took place during May 16-20, 2021. The conference was planned to take place in Cabourg, France, but changed to an online format due to the COVID-19 pandemic. The 45 papers included in this volume were carefully reviewed and selected from a total of 64 submissions. They were organized in topical sections named as follows: scale space and partial differential equations methods; flow, motion and registration; optimization theory and methods in imaging; machine learning in imaging; segmentation and labelling; restoration, reconstruction and interpolation; and inverse problems in imaging.