Author : Lizhen Ji
Publisher :
Page : 542 pages
File Size : 18,78 MB
Release : 2011
Category : Geometry, Analytic
ISBN : 9781571462244
Geometry and Analysis
Lizhen Ji
[PDF] Geometry And Analysis eBook
Geometry And Analysis Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Geometry And Analysis book. This book definitely worth reading, it is an incredibly well-written.
Differential Geometry and Analysis on CR Manifolds
Sorin Dragomir
Author : Sorin Dragomir
Publisher : Springer Science & Business Media
Page : 499 pages
File Size : 35,77 MB
Release : 2007-06-10
Category : Mathematics
ISBN : 0817644830
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
Topological Persistence in Geometry and Analysis
Leonid Polterovich
Author : Leonid Polterovich
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 37,7 MB
Release : 2020-05-11
Category : Education
ISBN : 1470454955
The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research. In particular, the authors present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, they discuss topological function theory, which provides new insight into oscillation of functions. The book is accessible to readers with a basic background in algebraic and differential topology.
Geometry, Analysis and Probability
Jean-Benoît Bost
Author : Jean-Benoît Bost
Publisher : Birkhäuser
Page : 363 pages
File Size : 40,72 MB
Release : 2017-04-26
Category : Mathematics
ISBN : 3319496387
This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.
Functional Analysis and Infinite-Dimensional Geometry
Marian Fabian
Author : Marian Fabian
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 36,58 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 1475734808
This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints.
Analysis and Geometry on Graphs and Manifolds
Matthias Keller
Author : Matthias Keller
Publisher : Cambridge University Press
Page : 493 pages
File Size : 37,13 MB
Release : 2020-08-20
Category : Mathematics
ISBN : 1108587380
This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides surveys of topics linking geometry, spectral theory and stochastics.
Asymptotic Geometric Analysis, Part I
Shiri Artstein-Avidan
Author : Shiri Artstein-Avidan
Publisher : American Mathematical Soc.
Page : 473 pages
File Size : 44,87 MB
Release : 2015-06-18
Category : Mathematics
ISBN : 1470421933
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality. The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more.
Qα Analysis on Euclidean Spaces
Jie Xiao
Author : Jie Xiao
Publisher : Walter de Gruyter GmbH & Co KG
Page : 230 pages
File Size : 36,57 MB
Release : 2019-03-18
Category : Mathematics
ISBN : 3110600285
Starting with the fundamentals of Qα spaces and their relationships to Besov spaces, this book presents all major results around Qα spaces obtained in the past 16 years. The applications of Qα spaces in the study of the incompressible Navier-Stokes system and its stationary form are also discussed. This self-contained book can be used as an essential reference for researchers and graduates in analysis and partial differential equations.
Complex Analysis and CR Geometry
Giuseppe Zampieri
Author : Giuseppe Zampieri
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 30,82 MB
Release : 2008
Category : Mathematics
ISBN : 0821844423
Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the $\bar\partial$-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometryrequires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting tograduate students who wish to learn it.
Analysis and Geometry on Groups
Nicholas T. Varopoulos
Author : Nicholas T. Varopoulos
Publisher : Cambridge University Press
Page : 172 pages
File Size : 39,98 MB
Release : 1993-01-07
Category : Mathematics
ISBN : 9780521353823
The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical, but are not concerned with what is described these days as real analysis. Most of the results described in this book have a dual formulation: they have a "discrete version" related to a finitely generated discrete group and a continuous version related to a Lie group. The authors chose to center this book around Lie groups, but could easily have pushed it in several other directions as it interacts with the theory of second order partial differential operators, and probability theory, as well as with group theory.