Non K Hler Complex Surfaces And Strongly Pseudoconcave Surfaces
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Non K Hler Complex Surfaces And Strongly Pseudoconcave Surfaces
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Author : Naohiko Kasuya
language : en
Publisher: Springer Nature
Release Date : 2025-03-14
Non K Hler Complex Surfaces And Strongly Pseudoconcave Surfaces written by Naohiko Kasuya and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-14 with Mathematics categories.
The main themes of this book are non-Kähler complex surfaces and strongly pseudoconcave complex surfaces. Though there are several notable examples of compact non-Kähler surfaces, including Hopf surfaces, Kodaira surfaces, and Inoue surfaces, these subjects have been regarded as secondary to Kähler manifolds and strongly pseudoconvex manifolds. Recently, however, the existence of uncountably many non-Kähler complex structures on the 4-dimensional Euclidean space has been shown by Di Scala, Kasuya, and Zuddas through their construction. Furthermore, Kasuya and Zuddas' handlebody construction reveals that strongly pseudoconcave surfaces have flexibility with respect to both four-dimensional topology and boundary contact structures. These constructions are based on the knowledge of differential topology and contact geometry, and provide examples of fruitful applications of these areas to complex geometry. Thus, for (especially non-compact) non-Kähler complex surfaces and strongly pseudoconcave complex surfaces, it is not an exaggeration to say that the research is still in its infancy, with numerous areas yet to be explored and expected to develop in the future.
Compact Complex Surfaces
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Author : W. Barth
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Compact Complex Surfaces written by W. Barth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Contents: Introduction. - Standard Notations. - Preliminaries. - Curves on Surfaces. - Mappings of Surfaces. - Some General Properties of Surfaces. - Examples. - The Enriques-Kodaira Classification. - Surfaces of General Type. - K3-Surfaces and Enriques Surfaces. - Bibliography. - Subject Index.
Compact Complex Surfaces
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Author : W. Barth
language : en
Publisher:
Release Date : 1984-05-01
Compact Complex Surfaces written by W. Barth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-05-01 with categories.
Non Complete Algebraic Surfaces
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Author : M. Miyanishi
language : en
Publisher:
Release Date : 2014-01-15
Non Complete Algebraic Surfaces written by M. Miyanishi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Compact Complex Surfaces
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Author : Wolf Barth
language : de
Publisher:
Release Date : 1984
Compact Complex Surfaces written by Wolf Barth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Complex manifolds categories.
Minimal Surfaces From A Complex Analytic Viewpoint
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Author : Antonio Alarcón
language : en
Publisher: Springer Nature
Release Date : 2021-03-10
Minimal Surfaces From A Complex Analytic Viewpoint written by Antonio Alarcón and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-10 with Mathematics categories.
This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann–Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi–Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.
Minimal Surfaces And Functions Of Bounded Variation
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Author : Giusti
language : en
Publisher: Springer Science & Business Media
Release Date : 1984-01-01
Minimal Surfaces And Functions Of Bounded Variation written by Giusti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-01 with Mathematics categories.
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].
Real Enriques Surfaces
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Author : Alexander Degtyarev
language : en
Publisher: Springer
Release Date : 2007-05-06
Real Enriques Surfaces written by Alexander Degtyarev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
This is the first attempt of a systematic study of real Enriques surfaces culminating in their classification up to deformation. Simple explicit topological invariants are elaborated for identifying the deformation classes of real Enriques surfaces. Some of theses are new and can be applied to other classes of surfaces or higher-dimensional varieties. Intended for researchers and graduate students in real algebraic geometry it may also interest others who want to become familiar with the field and its techniques. The study relies on topology of involutions, arithmetics of integral quadratic forms, algebraic geometry of surfaces, and the hyperkähler structure of K3-surfaces. A comprehensive summary of the necessary results and techniques from each of these fields is included. Some results are developed further, e.g., a detailed study of lattices with a pair of commuting involutions and a certain class of rational complex surfaces.
Enriques Surfaces I
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Author : François Cossec
language : en
Publisher: Springer
Release Date : 2025-01-24
Enriques Surfaces I written by François Cossec and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-24 with Mathematics categories.
This book, consisting of two volumes, gives a contemporary account of the study of the class of projective algebraic surfaces known as Enriques surfaces. These surfaces were discovered more than 125 years by F. Enriques in an attempt to extend the characterization of rational algebraic curves to the case of algebraic surfaces. The novel feature of the present exposition is that no assumption on the characteristic of the ground field is assumed. This requirement calls for exploring the geometry of such surfaces by purely geometric and arithmetic methods that do not rely on transcendental methods such as the theory of periods of algebraic surfaces of type K3, which are close relatives of Enriques surfaces. Some of the methods use many technical tools from algebraic geometry that are discussed in Volume 1 and may be a useful source of references for the study of algebraic surfaces over fields of positive characteristic. Volume 1 also contains a detailed exposition of the theory of elliptic surfaces over fields of arbitrary characteristic. The first volume is an essential and greatly extended revision of Enriques Surfaces I, published in 1989 by Birkhäuser and co-authored by F. Cossec and I. Dolgachev. Included is a new chapter devoted to the theory of moduli of Enriques surfaces. The two volumes together contain many examples and an extensive bibliography made up of more than 700 items.
Complex Algebraic Surfaces
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Author : A. Beauville
language : en
Publisher: Cambridge University Press
Release Date : 1983-09-08
Complex Algebraic Surfaces written by A. Beauville and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-09-08 with Mathematics categories.