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| Author | : Lan Ma |
| Publisher | : |
| Total Pages | : 80 |
| Release | : 1998 |
| Genre | : Cauchy-Riemann equations |
| ISBN | : |
| Author | : Francois Treves |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 133 |
| Release | : 1990 |
| Genre | : Cauchy-Riemann equations |
| ISBN | : 0821824961 |
This book presents a unified approach to homotopy formulas in the tangential Cauchy-Riemann complex, mainly on real hypersurfaces in complex space, but also on certain generic submanifolds of higher codimension. The construction combines the Bochner-Martinelli integral formulas with the FBI (Fourier-Bros-Iagolnitzer) minitransform. The hypersurface admits supporting manifolds of the appropriate holomorphic type from above and below. The supporting manifolds allow the selection of good phase functions and correspond to a kind of weak convexity in some directions, and concavity in others.
| Author | : Lan Ma |
| Publisher | : |
| Total Pages | : 74 |
| Release | : 1996 |
| Genre | : |
| ISBN | : |
| Author | : Gerald B. Folland |
| Publisher | : Princeton University Press |
| Total Pages | : 156 |
| Release | : 2016-03-02 |
| Genre | : Mathematics |
| ISBN | : 1400881528 |
Part explanation of important recent work, and part introduction to some of the techniques of modern partial differential equations, this monograph is a self-contained exposition of the Neumann problem for the Cauchy-Riemann complex and certain of its applications. The authors prove the main existence and regularity theorems in detail, assuming only a knowledge of the basic theory of differentiable manifolds and operators on Hilbert space. They discuss applications to the theory of several complex variables, examine the associated complex on the boundary, and outline other techniques relevant to these problems. In an appendix they develop the functional analysis of differential operators in terms of Sobolev spaces, to the extent it is required for the monograph.
| Author | : |
| Publisher | : |
| Total Pages | : 1100 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Kai Cieliebak |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 379 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821885332 |
This book is devoted to the interplay between complex and symplectic geometry in affine complex manifolds. Affine complex (a.k.a. Stein) manifolds have canonically built into them symplectic geometry which is responsible for many phenomena in complex geometry and analysis. The goal of the book is the exploration of this symplectic geometry (the road from 'Stein to Weinstein') and its applications in the complex geometric world of Stein manifolds (the road 'back').
| Author | : Steven G. Krantz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 2008-12-15 |
| Genre | : Mathematics |
| ISBN | : 0817646795 |
This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.
| Author | : John Willard Milnor |
| Publisher | : Princeton University Press |
| Total Pages | : 342 |
| Release | : 1974 |
| Genre | : Mathematics |
| ISBN | : 9780691081229 |
The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.
| Author | : Elisabetta Barletta |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 270 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821843044 |
The authors study the relationship between foliation theory and differential geometry and analysis on Cauchy-Riemann (CR) manifolds. The main objects of study are transversally and tangentially CR foliations, Levi foliations of CR manifolds, solutions of the Yang-Mills equations, tangentially Monge-Ampere foliations, the transverse Beltrami equations, and CR orbifolds. The novelty of the authors' approach consists in the overall use of the methods of foliation theory and choice of specific applications. Examples of such applications are Rea's holomorphic extension of Levi foliations, Stanton's holomorphic degeneracy, Boas and Straube's approximately commuting vector fields method for the study of global regularity of Neumann operators and Bergman projections in multi-dimensional complex analysis in several complex variables, as well as various applications to differential geometry. Many open problems proposed in the monograph may attract the mathematical community and lead to further applications of
| Author | : Chris Wendl |
| Publisher | : Springer |
| Total Pages | : 294 |
| Release | : 2018-06-28 |
| Genre | : Mathematics |
| ISBN | : 3319913719 |
This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
