Analysis and Geometry on Graphs and Manifolds

Analysis and Geometry on Graphs and Manifolds
Author: Matthias Keller
Publisher: Cambridge University Press
Total Pages: 493
Release: 2020-08-20
Genre: 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.

Analysis, Geometry, and Modeling in Finance

Analysis, Geometry, and Modeling in Finance
Author: Pierre Henry-Labordere
Publisher: CRC Press
Total Pages: 403
Release: 2008-09-22
Genre: Business & Economics
ISBN: 1420087002

Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approximate and partial solutions were previously available.Through the problem of option pricing, th

Analysis and Geometry on Groups

Analysis and Geometry on Groups
Author: Nicholas T. Varopoulos
Publisher: Cambridge University Press
Total Pages: 172
Release: 1993-01-07
Genre: 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.

An Introduction to Complex Analysis and Geometry

An Introduction to Complex Analysis and Geometry
Author: John P. D'Angelo
Publisher: American Mathematical Soc.
Total Pages: 177
Release: 2010
Genre: Functions of complex variables
ISBN: 0821852744

Provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics. The first four chapters provide an introduction to complex analysis with many elementary and unusual applications. Chapters 5 to 7 develop the Cauchy theory and include some striking applications to calculus. Chapter 8 glimpses several appealing topics, simultaneously unifying the book and opening the door to further study.

Asymptotic Geometric Analysis, Part I

Asymptotic Geometric Analysis, Part I
Author: Shiri Artstein-Avidan
Publisher: American Mathematical Soc.
Total Pages: 473
Release: 2015-06-18
Genre: 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.

Perspectives in Analysis, Geometry, and Topology

Perspectives in Analysis, Geometry, and Topology
Author: Ilia Itenberg
Publisher: Springer Science & Business Media
Total Pages: 483
Release: 2011-12-14
Genre: Mathematics
ISBN: 0817682775

The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.

Qα Analysis on Euclidean Spaces

Qα Analysis on Euclidean Spaces
Author: Jie Xiao
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 230
Release: 2019-03-18
Genre: 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.

New Trends on Analysis and Geometry in Metric Spaces

New Trends on Analysis and Geometry in Metric Spaces
Author: Fabrice Baudoin
Publisher: Springer Nature
Total Pages: 312
Release: 2022-02-04
Genre: Mathematics
ISBN: 3030841413

This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. Authored by leading experts in their fields, the lectures present different approaches to research topics with the common background of a relevant underlying, usually non-Riemannian, geometric structure. In particular, the topics covered concern differentiation and functions of bounded variation in metric spaces, Sobolev spaces, and differential geometry in the so-called Carnot–Carathéodory spaces. The text is based on lectures presented at the 10th School on "Analysis and Geometry in Metric Spaces" held in Levico Terme (TN), Italy, in collaboration with the University of Trento, Fondazione Bruno Kessler and CIME, Italy. The book is addressed to both graduate students and researchers.

The Analysis and Geometry of Hardy's Inequality

The Analysis and Geometry of Hardy's Inequality
Author: Alexander A. Balinsky
Publisher: Springer
Total Pages: 277
Release: 2015-10-20
Genre: Mathematics
ISBN: 3319228706

This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz’ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy’s Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.

Analysis and Geometry of Markov Diffusion Operators

Analysis and Geometry of Markov Diffusion Operators
Author: Dominique Bakry
Publisher: Springer Science & Business Media
Total Pages: 555
Release: 2013-11-18
Genre: Mathematics
ISBN: 3319002279

The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.