Supported Blow-Up and Prescribed Scalar Curvature on $S^n$, Man Chun Leung
Автор: Han Fei Et Al Название: Geometric Analysis Around Scalar Curvatures ISBN: 9813100540 ISBN-13(EAN): 9789813100541 Издательство: World Scientific Publishing Цена: 92930.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This volume contains three expanded lecture notes from the program Scalar Curvature in Manifold Topology and Conformal Geometry that was held at the Institute for Mathematical Sciences from 1 November to 31 December 2014. The first chapter surveys the recent developments on the fourth-order equations with negative exponent from geometric points of view such as positive mass theorem and uniqueness results. The next chapter deals with the recent important progress on several conjectures such as the existence of non-flat smooth hyper-surfaces and Serrin's over-determined problem. And the final chapter induces a new technique to handle the equation with critical index and the sign change coefficient as well as the negative index term. These topics will be of interest to those studying conformal geometry and geometric partial differential equations.
Автор: Manuel Ritor?; Vicente Miquel; Carlo Sinestrari; J Название: Mean Curvature Flow and Isoperimetric Inequalities ISBN: 303460212X ISBN-13(EAN): 9783034602129 Издательство: Springer Рейтинг: Цена: 27910.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Geometric flows have many applications in physics and geometry. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds.
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: 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: Martin R. Bridson; Andr? H?fliger Название: Metric Spaces of Non-Positive Curvature ISBN: 3642083994 ISBN-13(EAN): 9783642083990 Издательство: Springer Рейтинг: Цена: 111790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The purpose of this book is to describe the global properties of complete simply- connected spaces that are non-positively curved in the sense of A. D. Alexandrov and to examine the structure of groups that act properly on such spaces by isometries. Thus the central objects of study are metric spaces in which every pair of points can be joined by an arc isometric to a compact interval of the real line and in which every triangle satisfies the CAT(O) inequality. This inequality encapsulates the concept of non-positive curvature in Riemannian geometry and allows one to reflect the same concept faithfully in a much wider setting - that of geodesic metric spaces. Because the CAT(O) condition captures the essence of non-positive curvature so well, spaces that satisfy this condition display many of the elegant features inherent in the geometry of non-positively curved manifolds. There is therefore a great deal to be said about the global structure of CAT(O) spaces, and also about the structure of groups that act on them by isometries - such is the theme of this book. 1 The origins of our study lie in the fundamental work of A. D. Alexandrov .
Автор: Kichoon Yang Название: Complete Minimal Surfaces of Finite Total Curvature ISBN: 0792330129 ISBN-13(EAN): 9780792330127 Издательство: Springer Рейтинг: Цена: 71730.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Based on the idea that the study of complete minimal surfaces in R3 of finite total curvature amounts to the study of linear series on algebraic curves, this book offers an account of the Puncture Number Problem, which seeks to determine the possible underlying conformal structures for immersed complete minimal surfaces of finite total curvature.
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: A. Agrachev, D. Barilari, L. Rizzi Название: Curvature: A Variational Approach ISBN: 1470426463 ISBN-13(EAN): 9781470426460 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 65210.00 T Наличие на складе: Невозможна поставка. Описание: The curvature discussed in this paper is a far reaching generalization of the Riemannian sectional curvature. The authors give a unified definition of curvature which applies to a wide class of geometric structures whose geodesics arise from optimal control problems, including Riemannian, sub-Riemannian, Finsler and sub-Finsler spaces. Special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. The authors' construction of curvature is direct and naive, and similar to the original approach of Riemann. In particular, they extract geometric invariants from the asymptotics of the cost of optimal control problems. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.
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: George Isac; S?ndor Zolt?n N?meth Название: Scalar and Asymptotic Scalar Derivatives ISBN: 1441944842 ISBN-13(EAN): 9781441944849 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry and applied mathematics. The theoretical results are developed in particular with respect to the study of complementarity problems, monotonicity of nonlinear mappings and the non-gradient type monotonicity on Riemannian manifolds.
Автор: Fran?oise Dal`Bo; Marc Peign?; Andrea Sambusetti Название: Analytic and Probabilistic Approaches to Dynamics in Negative Curvature ISBN: 3319381172 ISBN-13(EAN): 9783319381176 Издательство: Springer Рейтинг: Цена: 79190.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The work consists of two introductory courses, developing different points of view on the study of the asymptotic behaviour of the geodesic flow, namely: the probabilistic approach via martingales and mixing (by Stephane Le Borgne);
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