The Bounded and Precise Word Problems for Presentations of Groups, S.V. Ivanov
Автор: Giusti Название: Minimal Surfaces and Functions of Bounded Variation ISBN: 0817631534 ISBN-13(EAN): 9780817631536 Издательство: Springer Рейтинг: Цена: 121110.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The problem of finding minimal surfaces, i. e. of finding the surface of least area among those bounded by a given curve, was one of the first considered after the foundation of the calculus of variations, and is one which received a satis- factory solution only in recent years. Called the problem of Plateau, after the blind physicist who did beautiful experiments with soap films and bubbles, it has resisted the efforts of many mathematicians for more than a century. It was only in the thirties that a solution was given to the problem of Plateau in 3-dimensional Euclidean space, with the papers of Douglas [DJ] and Rado [R T1, 2]. The methods of Douglas and Rado were developed and extended in 3-dimensions by several authors, but none of the results was shown to hold even for minimal hypersurfaces in higher dimension, let alone surfaces of higher dimension and codimension. It was not until thirty years later that the problem of Plateau was successfully attacked in its full generality, by several authors using measure-theoretic methods; in particular see De Giorgi [DG1, 2, 4, 5], Reifenberg [RE], Federer and Fleming [FF] and Almgren [AF1, 2]. Federer and Fleming defined a k-dimensional surface in IR as a k-current, i. e. a continuous linear functional on k-forms. Their method is treated in full detail in the splendid book of Federer [FH 1].
Автор: Nicola Gigli Название: Nonsmooth Differential Geometry-An Approach Tailored for Spaces with Ricci Curvature Bounded from Below ISBN: 1470427656 ISBN-13(EAN): 9781470427658 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 77610.00 T Наличие на складе: Невозможна поставка. Описание: The author discusses in which sense general metric measure spaces possess a first order differential structure. Building on this, spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting the author to define Hessian, covariant/exterior derivatives and Ricci curvature.
Автор: Daniel Beltita; Mihai Sabac Название: Lie Algebras of Bounded Operators ISBN: 3034895208 ISBN-13(EAN): 9783034895200 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In several proofs from the theory of finite-dimensional Lie algebras, an essential contribution comes from the Jordan canonical structure of linear maps acting on finite-dimensional vector spaces. On the other hand, there exist classical results concerning Lie algebras which advise us to use infinite-dimensional vector spaces as well.
Автор: Yichao Xu Название: Theory of Complex Homogeneous Bounded Domains ISBN: 9048165962 ISBN-13(EAN): 9789048165964 Издательство: Springer Рейтинг: Цена: 81050.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book is the first to systematically explore the classification and function theory of complex homogeneous bounded domains. Using the normal Siegel domains to realize the homogeneous bounded domains, we can obtain more property of the geometry and the function theory on homogeneous bounded domains.
This monograph presents the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Special emphasis is put on the new precise results on the L? extension of holomorphic functions in the past 5 years.
In Chapter 1, the classical questions of several complex variables motivating the development of this field are reviewed after necessary preparations from the basic notions of those variables and of complex manifolds such as holomorphic functions, pseudoconvexity, differential forms, and cohomology. In Chapter 2, the L? method of solving the d-bar equation is presented emphasizing its differential geometric aspect. In Chapter 3, a refinement of the Oka–Cartan theory is given by this method. The L? extension theorem with an optimal constant is included, obtained recently by Z. B?ocki and separately by Q.-A. Guan and X.-Y. Zhou. In Chapter 4, various results on the Bergman kernel are presented, including recent works of Maitani–Yamaguchi, Berndtsson, Guan–Zhou, and Berndtsson–Lempert. Most of these results are obtained by the L? method. In the last chapter, rather specific results are discussed on the existence and classification of certain holomorphic foliations and Levi flat hypersurfaces as their stables sets. These are also applications of the L? method obtained during the past 15 years.
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