Geometry and Analysis
Author: Lizhen Ji
Publisher:
Published: 2011
Total Pages: 542
ISBN-13: 9781571462244
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Differential Geometry and Analysis on CR Manifolds
Author: Sorin Dragomir
Publisher: Springer Science & Business Media
Published: 2007-06-10
Total Pages: 499
ISBN-13: 0817644830
DOWNLOAD EBOOKPresents 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
Author: Leonid Polterovich
Publisher: American Mathematical Soc.
Published: 2020-05-11
Total Pages: 128
ISBN-13: 1470454955
DOWNLOAD EBOOKThe 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.
Analysis and Geometry on Graphs and Manifolds
Author: Matthias Keller
Publisher: Cambridge University Press
Published: 2020-08-20
Total Pages: 493
ISBN-13: 1108587380
DOWNLOAD EBOOKThis 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.
Functional Analysis and Infinite-Dimensional Geometry
Author: Marian Fabian
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 455
ISBN-13: 1475734808
DOWNLOAD EBOOKThis 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.
Geometry, Analysis and Probability
Author: Jean-Benoît Bost
Publisher: Birkhäuser
Published: 2017-04-26
Total Pages: 363
ISBN-13: 3319496387
DOWNLOAD EBOOKThis 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.
Groups and Geometric Analysis
Author: Sigurdur Helgason
Publisher: American Mathematical Society
Published: 2022-03-17
Total Pages: 667
ISBN-13: 0821832115
DOWNLOAD EBOOKGroup-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group. The introductory chapter is a self-contained account of the analysis on surfaces of constant curvature. Later chapters cover general cases of the Radon transform, spherical functions, invariant operators, compact symmetric spaces and other topics. This book, together with its companion volume, Geometric Analysis on Symmetric Spaces (AMS Mathematical Surveys and Monographs series, vol. 39, 1994), has become the standard text for this approach to geometric analysis. Sigurdur Helgason was awarded the Steele Prize for outstanding mathematical exposition for Groups and Geometric Analysis and Differential Geometry, Lie Groups and Symmetric Spaces.
Complex Analysis and CR Geometry
Author: Giuseppe Zampieri
Publisher: American Mathematical Soc.
Published: 2008
Total Pages: 210
ISBN-13: 0821844423
DOWNLOAD EBOOKCauchy-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.
Asymptotic Geometric Analysis, Part I
Author: Shiri Artstein-Avidan
Publisher: American Mathematical Soc.
Published: 2015-06-18
Total Pages: 473
ISBN-13: 1470421933
DOWNLOAD EBOOKThe 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
Author: Jie Xiao
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2019-03-18
Total Pages: 230
ISBN-13: 3110600285
DOWNLOAD EBOOKStarting 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.
