Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces, Luigi Ambrosio, Andrea Mondino, Giuseppe Savare
Автор: Owen Dearricott; Fernando Galaz-Garc?a; Lee Kennar Название: Geometry of Manifolds with Non-negative Sectional Curvature ISBN: 3319063723 ISBN-13(EAN): 9783319063720 Издательство: Springer Рейтинг: Цена: 32600.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Riemannian manifolds with positive sectional curvature.- An introduction to isometric group actions.- A note on maximal symmetry rank, quasipositive curvature and low dimensional manifolds.- Lectures on n-Sasakian manifolds.- On the Hopf conjecture with symmetry.- An Introduction to Exterior Differential Systems.
Автор: Rafael L?pez Название: Constant Mean Curvature Surfaces with Boundary ISBN: 3662512564 ISBN-13(EAN): 9783662512562 Издательство: Springer Рейтинг: Цена: 79190.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields.
While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of "compact surfaces with boundaries," narrowing its focus to a geometric view. Basic issues include the discussion whether the symmetries of the curve inherit to the surface; the possible values of the mean curvature, area and volume; stability; the circular boundary case and the existence of the Plateau problem in the non-parametric case. The exposition provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambient spaces. Throughout the text, numerous illustrations clarify the results and their proofs.
The book is intended for graduate students and researchers in the field of differential geometry and especially theory of surfaces, including geometric analysis and geometric PDEs. It guides readers up to the state-of-the-art of the theory and introduces them to interesting open problems.
Автор: Laurent Najman; Pascal Romon Название: Modern Approaches to Discrete Curvature ISBN: 3319580019 ISBN-13(EAN): 9783319580012 Издательство: Springer Рейтинг: Цена: 60550.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics.
Автор: Aravinda Название: Geometry, Topology, and Dynamics in Negative Curvature ISBN: 110752900X ISBN-13(EAN): 9781107529007 Издательство: Cambridge Academ Рейтинг: Цена: 76030.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Negative curvature arises in several mathematical areas, including geometry, topology, dynamics, and number theory. This volume contains survey articles around this common theme, which should help mathematicians interested in transitioning between these areas, as well as graduate students entering this interdisciplinary subject.
Автор: Carlo Mantegazza Название: Lecture Notes on Mean Curvature Flow ISBN: 3034803400 ISBN-13(EAN): 9783034803403 Издательство: Springer Рейтинг: Цена: 93160.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This introduction to the subject of mean curvature flow of hypersurfaces has a special emphasis on the analysis of singularities and provides a detailed discussion of the classical parametric approach mainly developed by R. Hamilton and G. Huisken.
Автор: Yoshihiro Tonegawa Название: Brakke`s Mean Curvature Flow ISBN: 9811370745 ISBN-13(EAN): 9789811370748 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book explains the notion of Brakke`s mean curvature flow and its existence and regularity theories without assuming familiarity with geometric measure theory.
Автор: Sutherland, Wilson A Название: Introduction to Metric and Topological Spaces ISBN: 019956308X ISBN-13(EAN): 9780199563081 Издательство: Oxford Academ Рейтинг: Цена: 45400.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This fully updated new edition of Wilson Sutherland`s classic text, Introduction to Metric and Topological Spaces, establishes the language of metric and topological spaces with continuity as the motivating concept, before developing its discussion to cover compactness, connectedness, and completeness.
Автор: Jan Rataj; Martina Z?hle Название: Curvature Measures of Singular Sets ISBN: 3030181820 ISBN-13(EAN): 9783030181826 Издательство: Springer Рейтинг: Цена: 121110.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
The book describes how curvature measures can be introduced for certain classes of sets with singularities in Euclidean spaces. Its focus lies on sets with positive reach and some extensions, which include the classical polyconvex sets and piecewise smooth submanifolds as special cases. The measures under consideration form a complete system of certain Euclidean invariants. Techniques of geometric measure theory, in particular, rectifiable currents are applied, and some important integral-geometric formulas are derived. Moreover, an approach to curvatures for a class of fractals is presented, which uses approximation by the rescaled curvature measures of small neighborhoods. The book collects results published during the last few decades in a nearly comprehensive way.
Автор: Jos? M. Maz?n; Julio Daniel Rossi; J. Juli?n Toled Название: Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets ISBN: 3030062422 ISBN-13(EAN): 9783030062422 Издательство: Springer Рейтинг: Цена: 51230.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book highlights the latest developments in the geometry of measurable sets, presenting them in simple, straightforward terms. It addresses nonlocal notions of perimeter and curvature and studies in detail the minimal surfaces associated with them. These notions of nonlocal perimeter and curvature are defined on the basis of a non-singular kernel. Further, when the kernel is appropriately rescaled, they converge toward the classical perimeter and curvature as the rescaling parameter tends to zero. In this way, the usual notions can be recovered by using the nonlocal ones. In addition, nonlocal heat content is studied and an asymptotic expansion is obtained. Given its scope, the book is intended for undergraduate and graduate students, as well as senior researchers interested in analysis and/or geometry.
With contributions by leading experts in geometric analysis, this volume is documenting the material presented in the John H. Barrett Memorial Lectures held at the University of Tennessee, Knoxville, on May 29 - June 1, 2018. The central topic of the 2018 lectures was mean curvature flow, and the material in this volume covers all recent developments in this vibrant area that combines partial differential equations with differential geometry.
Автор: Heinonen Название: Sobolev Spaces on Metric Measure Spaces ISBN: 1107092345 ISBN-13(EAN): 9781107092341 Издательство: Cambridge Academ Рейтинг: Цена: 132000.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Analysis on metric spaces is a field that has expanded dramatically since the 1990s. Written by some of the founders of the theory, this book provides a coherent treatment from first principles. It is an ideal introduction for graduate students and a useful reference for experts in the field.
Автор: Yeh, James J. Название: Metric in measure spaces ISBN: 9813200391 ISBN-13(EAN): 9789813200395 Издательство: World Scientific Publishing Рейтинг: Цена: 95040.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Measure and metric are two fundamental concepts in measuring the size of a mathematical object. Yet there has been no systematic investigation of this relation. The book closes this gap.
Contents: Measure and Outer Measure; Construction of Outer Measures; Borel Measures; Hausdorff Measures; Covering Theorems; Differentiation of Measures; Averaging Operators and Differentiation of Integrals; Lebesgue Differentiation Theorem for Integrals; Hardy-Littlewood Maximal Functions; Density of Sets; Approximate Limit and Approximate Continuity; Lipschitz Mappings;
Readership: Mathematicians and graduate students in mathematics.
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