A Generalization of Riemann Mappings and Geometric Structures on a Space of Domains in C$^n$


Book Description

Similar in philosophy to the study of moduli spaces in algebraic geometry, the central theme of this book is that spaces of (pseudoconvex) domains should admit geometrical structures that reflect the complex geometry of the underlying domains in a natural way. With its unusual geometric perspective of some topics in several complex variables, this book appeals to those who view much of mathematics in broadly geometrical terms.







Real Methods in Complex and CR Geometry


Book Description

The geometry of real submanifolds in complex manifolds and the analysis of their mappings belong to the most advanced streams of contemporary Mathematics. In this area converge the techniques of various and sophisticated mathematical fields such as P.D.E.s, boundary value problems, induced equations, analytic discs in symplectic spaces, complex dynamics. For the variety of themes and the surprisingly good interplaying of different research tools, these problems attracted the attention of some among the best mathematicians of these latest two decades. They also entered as a refined content of an advanced education. In this sense the five lectures of this volume provide an excellent cultural background while giving very deep insights of current research activity.




Function Spaces in Analysis


Book Description

This volume contains the proceedings of the Seventh Conference on Function Spaces, which was held from May 20-24, 2014 at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.




Moduli Spaces of Riemann Surfaces


Book Description

Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.




Complex Analysis and Geometry


Book Description

This meeting has been motivated by two events: the 85th birthday of Pierre Lelong, and the end of the third year of the European network "Complex analysis and analytic geometry" from the programme Human Capital and Mobility. For the first event, Mathematicians from Poland, Sweden, United States and France, whose work is particularly related to the one ofP. Lelong have accepted to participate; for the second, the different teams of the Network sent lecturers to report on their most recent works. These teams are from Grenoble, Wuppertal, Berlin, Pisa and Paris VI; in fact, most of their results are also related to Lelong's work and, a posteriori, it is difficult to decide whether a talk is motivated by the first or by the second event. We chose only plenary lectures, usually of one hour, except a small number, given by young mathematicians, which have been shorter. A two hours problem session has been organized. The Proceedings gather papers which are exact texts of the talks, or are closely related to them. The members from the Network and five other lecturers sent us papers; the other lecturers published the content of their talks in mathematical Journals. All the presented texts have been submitted to referees independent of the organizing committee; the texts of the problems have been approved by their authors.




Seminari di geometria


Book Description




Geometric Complex Analysis - Proceedings Of The Third International Research Institute Of Mathematical Society Of Japan


Book Description

This proceedings is a collection of articles in several complex variables with emphasis on geometric methods and results, which includes several survey papers reviewing the development of the topics in these decades. Through this volume one can see an active field providing insight into other fields like algebraic geometry, dynamical systems and partial differential equations.




The Geometry and Topology of Three-Manifolds


Book Description

William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume IV contains Thurston's highly influential, though previously unpublished, 1977–78 Princeton Course Notes on the Geometry and Topology of 3-manifolds. It is an indispensable part of the Thurston collection but can also be used on its own as a textbook or for self-study.




Advanced Courses Of Mathematical Analysis V - Proceedings Of The Fifth International School


Book Description

This volume contains recent papers by several specialists in different fields of mathematical analysis. It offers a reasonably wide perspective of the current state of research, and new trends, in areas related to measure theory, harmonic analysis, non-associative structures in functional analysis and summability in locally convex spaces.Those interested in researching any areas of mathematical analysis will find here numerous suggestions on possible topics with an important impact today. Often, the contributions are presented in an expository nature and this makes the discussed topics accessible to a more general audience.