• Mathematics

Differential Geometry and Analysis on CR Manifolds


Author: Sorin Dragomir,Giuseppe Tomassini
Publisher: Springer Science & Business Media
ISBN: 9780817644833
Category: Mathematics
Page: 488
View: 7035
Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis are employed in CR geometry Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook Provides unproved statements and comments inspiring further study

    • Mathematics

Fully Nonlinear PDEs in Real and Complex Geometry and Optics

Cetraro, Italy 2012, Editors: Cristian E. Gutiérrez, Ermanno Lanconelli
Author: Luca Capogna,Pengfei Guan,Cristian E. Gutiérrez,Annamaria Montanari
Publisher: Springer
ISBN: 3319009427
Category: Mathematics
Page: 210
View: 7326
The purpose of this CIME summer school was to present current areas of research arising both in the theoretical and applied setting that involve fully nonlinear partial different equations. The equations presented in the school stem from the fields of Conformal Mapping Theory, Differential Geometry, Optics, and Geometric Theory of Several Complex Variables. The school consisted of four courses: Extremal problems for quasiconformal mappings in space by Luca Capogna, Fully nonlinear equations in geometry by Pengfei Guan, Monge-Ampere type equations and geometric optics by Cristian E. Gutiérrez, and On the Levi Monge Ampere equation by Annamaria Montanari.

    • Mathematics

Geometry of Cauchy-Riemann Submanifolds


Author: Sorin Dragomir,Mohammad Hasan Shahid,Falleh R. Al-Solamy
Publisher: Springer
ISBN: 9811009163
Category: Mathematics
Page: 390
View: 4558
This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds. Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.

    • Mathematics

Differential Geometry of Lightlike Submanifolds


Author: Krishan Duggal,Bayram Sahin
Publisher: Springer Science & Business Media
ISBN: 9783034602518
Category: Mathematics
Page: 488
View: 2074
Since the second half of the 20th century, the Riemannian and semi-Riemannian geometries have been active areas of research in di?erential geometry and its - plications to a variety of subjects in mathematics and physics. A recent survey in Marcel Berger’s book [60] includes the major developments of Riemannian ge- etry since 1950, citing the works of di?erential geometers of that time. During the mid 1970s, the interest shifted towards Lorentzian geometry, the mathematical theory used in general relativity. Since then there has been an amazing leap in the depth of the connection between modern di?erential geometry and mathematical relativity, both from the local and the global point of view. Most of the work on global Lorentzian geometry has been described in a standard book by Beem and Ehrlich [34] and in their second edition in 1996, with Easley. As for any semi-Riemannian manifold there is a natural existence of null (lightlike)subspaces, in 1996,Duggal-Bejancupublished a book[149] on the lig- like (degenerate) geometry of submanifolds needed to ?ll an important missing part in the general theory of submanifolds. Since then the large number of papers published on lightlike hypersurfaces and general theory of submanifolds of semi- Riemannian manifolds has created a demand for publication of this volume as an update on the study of lightlike geometry. The objective is to focus on all new geometric results (in particular, those availableonlyafterpublicationoftheDuggal–Bejancubook)onlightlikegeometry with proofs and their physical applications in mathematical physics.

    • Mathematics

Trends in Harmonic Analysis


Author: Massimo A. Picardello
Publisher: Springer Science & Business Media
ISBN: 8847028531
Category: Mathematics
Page: 448
View: 6770
This book illustrates the wide range of research subjects developed by the Italian research group in harmonic analysis, originally started by Alessandro Figà-Talamanca, to whom it is dedicated in the occasion of his retirement. In particular, it outlines some of the impressive ramifications of the mathematical developments that began when Figà-Talamanca brought the study of harmonic analysis to Italy; the research group that he nurtured has now expanded to cover many areas. Therefore the book is addressed not only to experts in harmonic analysis, summability of Fourier series and singular integrals, but also in potential theory, symmetric spaces, analysis and partial differential equations on Riemannian manifolds, analysis on graphs, trees, buildings and discrete groups, Lie groups and Lie algebras, and even in far-reaching applications as for instance cellular automata and signal processing (low-discrepancy sampling, Gaussian noise).

    • Mathematics

Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 2422


    • Mathematics

Sub-Riemannian Geometry


Author: Andre Bellaiche,Jean-Jaques Risler
Publisher: Birkhäuser
ISBN: 3034892101
Category: Mathematics
Page: 398
View: 1596



    • Mathematics

Spherical Tube Hypersurfaces


Author: Alexander Isaev
Publisher: Springer
ISBN: 3642197833
Category: Mathematics
Page: 230
View: 5184
We consider Levi non-degenerate tube hypersurfaces in complex linear space which are "spherical", that is, locally CR-equivalent to the real hyperquadric. Spherical hypersurfaces are characterized by the condition of the vanishing of the CR-curvature form, so such hypersurfaces are flat from the CR-geometric viewpoint. On the other hand, such hypersurfaces are of interest from the point of view of affine geometry. Thus our treatment of spherical tube hypersurfaces in this book is two-fold: CR-geometric and affine-geometric. Spherical tube hypersurfaces turn out to possess remarkable properties. For example, every such hypersurface is real-analytic and extends to a closed real-analytic spherical tube hypersurface in complex space. One of our main goals is to give an explicit affine classification of closed spherical tube hypersurfaces whenever possible. In this book we offer a comprehensive exposition of the theory of spherical tube hypersurfaces starting with the idea proposed in the pioneering work by P. Yang (1982) and ending with the new approach due to G. Fels and W. Kaup (2009).

    • Mathematics

Seminar on Stochastic Analysis, Random Fields and Applications

Centro Stefano Franscini, Ascona, September 1996
Author: Robert C. Dalang,Marco Dozzi,Francesco Russo
Publisher: Springer Science & Business Media
ISBN: 9783764361068
Category: Mathematics
Page: 300
View: 4403
A collection of 20 refereed research or review papers presented at a six-day seminar in Switzerland. The contributions focus on stochastic analysis, its applications to the engineering sciences, and stochastic methods in financial models, which was the subject of a minisymposium.

    • Mathematics

Real Submanifolds in Complex Space and Their Mappings (PMS-47)


Author: M. Salah Baouendi,Peter Ebenfelt,Linda Preiss Rothschild
Publisher: Princeton University Press
ISBN: 1400883962
Category: Mathematics
Page: 416
View: 7259
This book presents many of the main developments of the past two decades in the study of real submanifolds in complex space, providing crucial background material for researchers and advanced graduate students. The techniques in this area borrow from real and complex analysis and partial differential equations, as well as from differential, algebraic, and analytical geometry. In turn, these latter areas have been enriched over the years by the study of problems in several complex variables addressed here. The authors, M. Salah Baouendi, Peter Ebenfelt, and Linda Preiss Rothschild, include extensive preliminary material to make the book accessible to nonspecialists. One of the most important topics that the authors address here is the holomorphic extension of functions and mappings that satisfy the tangential Cauchy-Riemann equations on real submanifolds. They present the main results in this area with a novel and self-contained approach. The book also devotes considerable attention to the study of holomorphic mappings between real submanifolds, and proves finite determination of such mappings by their jets under some optimal assumptions. The authors also give a thorough comparison of the various nondegeneracy conditions for manifolds and mappings and present new geometric interpretations of these conditions. Throughout the book, Cauchy-Riemann vector fields and their orbits play a central role and are presented in a setting that is both general and elementary.

    • Mathematics

Complex Analysis and Geometry


Author: Vincenzo Ancona,Edoardo Ballico,A. Silva
Publisher: CRC Press
ISBN: 9780824796723
Category: Mathematics
Page: 576
View: 7552
Based on a conference held in Trento, Italy, and sponsored by the Centro Internazionale per la Ricera Matematica, this work presents advances in several complex variables and related topics such as transcendental algebraic geometry, infinite dimensional supermanifolds, and foliations. It covers the unfoldings of singularities, Levi foliations, Cauchy-Reimann manifolds, infinite dimensional supermanifolds, conformal structures, algebraic groups, instantons and more.

    • Mathematics

Geometry and Complex Variables


Author: S. Coen
Publisher: CRC Press
ISBN: 9780824784454
Category: Mathematics
Page: 520
View: 8148


    • Mathematics

Metric and Differential Geometry

The Jeff Cheeger Anniversary Volume
Author: Xianzhe Dai,Xiaochun Rong
Publisher: Springer Science & Business Media
ISBN: 3034802579
Category: Mathematics
Page: 364
View: 1433
Metric and Differential Geometry grew out of a similarly named conference held at Chern Institute of Mathematics, Tianjin and Capital Normal University, Beijing. The various contributions to this volume cover a broad range of topics in metric and differential geometry, including metric spaces, Ricci flow, Einstein manifolds, Kähler geometry, index theory, hypoelliptic Laplacian and analytic torsion. It offers the most recent advances as well as surveys the new developments. Contributors: M.T. Anderson J.-M. Bismut X. Chen X. Dai R. Harvey P. Koskela B. Lawson X. Ma R. Melrose W. Müller A. Naor J. Simons C. Sormani D. Sullivan S. Sun G. Tian K. Wildrick W. Zhang


    • Mathematics

Partial Differential Equations in Several Complex Variables


Author: So-Chin Chen,Mei-Chi Shaw
Publisher: American Mathematical Soc.
ISBN: 9780821829615
Category: Mathematics
Page: 380
View: 9036
This book is intended both as an introductory text and as a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the fields of Cauchy-Riemann and tangential Cauchy-Riemann operators. This book gives an up-to-date account of the theories for these equations and their applications. The background material in several complex variables is developed in the first three chapters, leading to the Levi problem. The next three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the $\bar\partial$-Neumann problem, including $L^2$ existence theorems on pseudoconvex domains, $\frac 12$-subelliptic estimates for the $\bar\partial$-Neumann problems on strongly pseudoconvex domains, global regularity of $\bar\partial$ on more general pseudoconvex domains, boundary regularity of biholomorphic mappings, irregularity of the Bergman projection on worm domains. The second part of the book gives a comprehensive study of the tangential Cauchy-Riemann equations. Chapter 7 introduces the tangential Cauchy-Riemann complex and the Lewy equation. An extensive account of the $L^2$ theory for $\square_b$ and $\bar\partial_b$ is given in Chapters 8 and 9. Explicit integral solution representations are constructed both on the Heisenberg groups and on strictly convex boundaries with estimates in Holder and $L^p$ spaces. Embeddability of abstract $CR$ structures is discussed in detail in the last chapter. This self-contained book provides a much-needed introductory text to several complex variables and partial differential equations. It is also a rich source of information to experts.

    • Mathematics

Isomonodromic Deformations and Frobenius Manifolds

An Introduction
Author: Claude Sabbah
Publisher: Springer Science & Business Media
ISBN: 9781848000544
Category: Mathematics
Page: 279
View: 4305
Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations. It ends with applications to recent research questions related to mirror symmetry. The fundamental tool used is that of a vector bundle with connection. The book includes complete proofs, and applications to recent research questions. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry.