An Introduction To The Analysis Of Paths On A Riemannian Manifold

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An Introduction to the Analysis of Paths on a Riemannian Manifold

Daniel W. Stroock
An Introduction to the Analysis of Paths on a Riemannian Manifold Book PDF

Author : Daniel W. Stroock
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 44,8 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821838396

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An Introduction to the Analysis of Paths on a Riemannian Manifold by Daniel W. Stroock Pdf

Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR.

The Laplacian on a Riemannian Manifold

Steven Rosenberg
The Laplacian on a Riemannian Manifold Book PDF

Author : Steven Rosenberg
Publisher : Cambridge University Press
Page : 190 pages
File Size : 43,7 Mb
Release : 1997-01-09
Category : Mathematics
ISBN : 0521468310

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The Laplacian on a Riemannian Manifold by Steven Rosenberg Pdf

This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.

The Laplacian on a Riemannian Manifold

Steven Rosenberg
The Laplacian on a Riemannian Manifold Book PDF

Author : Steven Rosenberg
Publisher : Unknown
Page : 185 pages
File Size : 43,5 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107362067

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The Laplacian on a Riemannian Manifold by Steven Rosenberg Pdf

This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.

Analysis, Geometry and Quantum Field Theory

Clara L. Aldana
Analysis Geometry and Quantum Field Theory Book PDF

Author : Clara L. Aldana
Publisher : American Mathematical Soc.
Page : 271 pages
File Size : 44,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821891445

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Analysis, Geometry and Quantum Field Theory by Clara L. Aldana Pdf

This volume contains the proceedings of the conference ``Analysis, Geometry and Quantum Field Theory'' held at Potsdam University in September 2011, which honored Steve Rosenberg's 60th birthday. The papers in this volume cover a wide range of areas, including Quantum Field Theory, Deformation Quantization, Gerbes, Loop Spaces, Index Theory, Determinants of Elliptic Operators, K-theory, Infinite Rank Bundles and Mathematical Biology.

Maximum Principles on Riemannian Manifolds and Applications

Stefano Pigola,Marco Rigoli,Alberto Giulio Setti
Maximum Principles on Riemannian Manifolds and Applications Book PDF

Author : Stefano Pigola,Marco Rigoli,Alberto Giulio Setti
Publisher : American Mathematical Soc.
Page : 99 pages
File Size : 42,8 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821836392

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Maximum Principles on Riemannian Manifolds and Applications by Stefano Pigola,Marco Rigoli,Alberto Giulio Setti Pdf

The aim of this paper is to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity recently obtained by the authors. Applications are given to a number of geometrical problems in the setting of complete Riemannian manifolds, under assumptions either on the curvature or on the volume growth of geodesic balls.

Stochastic Analysis on Manifolds

Elton P. Hsu
Stochastic Analysis on Manifolds Book PDF

Author : Elton P. Hsu
Publisher : American Mathematical Soc.
Page : 297 pages
File Size : 50,8 Mb
Release : 2002
Category : Differential geometry
ISBN : 9780821808023

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Stochastic Analysis on Manifolds by Elton P. Hsu Pdf

Concerned with probability theory, Elton Hsu's study focuses primarily on the relations between Brownian motion on a manifold and analytical aspects of differential geometry. A key theme is the probabilistic interpretation of the curvature of a manifold

Isometric Embedding of Riemannian Manifolds in Euclidean Spaces

Qing Han,Jia-Xing Hong
Isometric Embedding of Riemannian Manifolds in Euclidean Spaces Book PDF

Author : Qing Han,Jia-Xing Hong
Publisher : American Mathematical Soc.
Page : 278 pages
File Size : 40,5 Mb
Release : 2006
Category : Algebraic spaces
ISBN : 9780821840719

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Isometric Embedding of Riemannian Manifolds in Euclidean Spaces by Qing Han,Jia-Xing Hong Pdf

The question of the existence of isometric embeddings of Riemannian manifolds in Euclidean space is already more than a century old. This book presents, in a systematic way, results both local and global and in arbitrary dimension but with a focus on the isometric embedding of surfaces in ${\mathbb R}^3$. The emphasis is on those PDE techniques which are essential to the most important results of the last century. The classic results in this book include the Janet-Cartan Theorem, Nirenberg's solution of the Weyl problem, and Nash's Embedding Theorem, with a simplified proof by Gunther. The book also includes the main results from the past twenty years, both local and global, on the isometric embedding of surfaces in Euclidean 3-space. The work will be indispensable to researchers in the area. Moreover, the authors integrate the results and techniques into a unified whole, providing a good entry point into the area for advanced graduate students or anyone interested in this subject. The authors avoid what is technically complicated. Background knowledge is kept to an essential minimum: a one-semester course in differential geometry and a one-year course in partial differential equations.

The Ubiquitous Heat Kernel

Jay Jorgenson,American Mathematical Society
The Ubiquitous Heat Kernel Book PDF

Author : Jay Jorgenson,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 47,7 Mb
Release : 2006
Category : Geometry, Algebraic
ISBN : 9780821836989

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The Ubiquitous Heat Kernel by Jay Jorgenson,American Mathematical Society Pdf

The aim of this volume is to bring together research ideas from various fields of mathematics which utilize the heat kernel or heat kernel techniques in their research. The intention of this collection of papers is to broaden productive communication across mathematical sub-disciplines and to provide a vehicle which would allow experts in one field to initiate research with individuals in another field, as well as to give non-experts a resource which can facilitate expanding theirresearch and connecting with others.

Analysis for Diffusion Processes on Riemannian Manifolds

Feng-Yu Wang
Analysis for Diffusion Processes on Riemannian Manifolds Book PDF

Author : Feng-Yu Wang
Publisher : World Scientific
Page : 392 pages
File Size : 52,6 Mb
Release : 2014
Category : Mathematics
ISBN : 9789814452656

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Analysis for Diffusion Processes on Riemannian Manifolds by Feng-Yu Wang Pdf

Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.

Geometric Control Theory and Sub-Riemannian Geometry

Gianna Stefani,Ugo Boscain,Jean-Paul Gauthier,Andrey Sarychev,Mario Sigalotti
Geometric Control Theory and Sub Riemannian Geometry Book PDF

Author : Gianna Stefani,Ugo Boscain,Jean-Paul Gauthier,Andrey Sarychev,Mario Sigalotti
Publisher : Springer
Page : 385 pages
File Size : 55,7 Mb
Release : 2014-06-05
Category : Mathematics
ISBN : 9783319021324

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Geometric Control Theory and Sub-Riemannian Geometry by Gianna Stefani,Ugo Boscain,Jean-Paul Gauthier,Andrey Sarychev,Mario Sigalotti Pdf

Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.

Séminaire de Probabilités XLIII

Catherine Donati Martin,Antoine Lejay,Alain Rouault
S minaire de Probabilit s XLIII Book PDF

Author : Catherine Donati Martin,Antoine Lejay,Alain Rouault
Publisher : Springer
Page : 503 pages
File Size : 42,9 Mb
Release : 2010-10-20
Category : Mathematics
ISBN : 9783642152177

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Séminaire de Probabilités XLIII by Catherine Donati Martin,Antoine Lejay,Alain Rouault Pdf

This is a new volume of the Séminaire de Probabilités which is now in its 43rd year. Following the tradition, this volume contains about 20 original research and survey articles on topics related to stochastic analysis. It contains an advanced course of J. Picard on the representation formulae for fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differential equations, stochastic differential geometry, filtrations, analysis on Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journées de Probabilités held in Poitiers in June 2009.

Elements of Stochastic Calculus and Analysis

Daniel W. Stroock
Elements of Stochastic Calculus and Analysis Book PDF

Author : Daniel W. Stroock
Publisher : Springer
Page : 206 pages
File Size : 54,8 Mb
Release : 2018-04-24
Category : Mathematics
ISBN : 9783319770383

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Elements of Stochastic Calculus and Analysis by Daniel W. Stroock Pdf

This book gives a somewhat unconventional introduction to stochastic analysis. Although most of the material coveredhere has appeared in other places, this book attempts to explain the core ideas on which that material is based. As a consequence, the presentation is more an extended mathematical essay than a ``definition,lemma, theorem'' text. In addition, it includes several topics that are not usually treated elsewhere. For example,Wiener's theory of homogeneous chaos is discussed, Stratovich integration is given a novel development and applied to derive Wong and Zakai's approximation theorem, and examples are given of the application ofMalliavin's calculus to partial differential equations. Each chapter concludes with several exercises, some of which are quite challenging. The book is intended for use by advanced graduate students and researchmathematicians who may be familiar with many of the topics but want to broaden their understanding of them.

Covariant Schrödinger Semigroups on Riemannian Manifolds

Batu Güneysu
Covariant Schr dinger Semigroups on Riemannian Manifolds Book PDF

Author : Batu Güneysu
Publisher : Birkhäuser
Page : 239 pages
File Size : 46,9 Mb
Release : 2017-12-22
Category : Mathematics
ISBN : 9783319689036

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Covariant Schrödinger Semigroups on Riemannian Manifolds by Batu Güneysu Pdf

This monograph discusses covariant Schrödinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the fact that the existing literature on Schrödinger operators has mainly focused on scalar Schrödinger operators on Euclidean spaces so far. In particular, the book studies operators that act on sections of vector bundles. In addition, these operators are allowed to have unbounded potential terms, possibly with strong local singularities. The results presented here provide the first systematic study of such operators that is sufficiently general to simultaneously treat the natural operators from quantum mechanics, such as magnetic Schrödinger operators with singular electric potentials, and those from geometry, such as squares of Dirac operators that have smooth but endomorphism-valued and possibly unbounded potentials. The book is largely self-contained, making it accessible for graduate and postgraduate students alike. Since it also includes unpublished findings and new proofs of recently published results, it will also be interesting for researchers from geometric analysis, stochastic analysis, spectral theory, and mathematical physics..

The Ricci Flow: An Introduction

Bennett Chow,Dan Knopf
The Ricci Flow An Introduction Book PDF

Author : Bennett Chow,Dan Knopf
Publisher : American Mathematical Soc.
Page : 342 pages
File Size : 48,7 Mb
Release : 2004
Category : Global differential geometry
ISBN : 9780821835159

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The Ricci Flow: An Introduction by Bennett Chow,Dan Knopf Pdf

The Ricci flow is a powerful technique that integrates geometry, topology, and analysis. Intuitively, the idea is to set up a PDE that evolves a metric according to its Ricci curvature. The resulting equation has much in common with the heat equation, which tends to 'flow' a given function to ever nicer functions. By analogy, the Ricci flow evolves an initial metric into improved metrics. Richard Hamilton began the systematic use of the Ricci flow in the early 1980s and applied it in particular to study 3-manifolds. Grisha Perelman has made recent breakthroughs aimed at completing Hamilton's program. The Ricci flow method is now central to our understanding of the geometry and topology of manifolds.This book is an introduction to that program and to its connection to Thurston's geometrization conjecture. The authors also provide a 'Guide for the hurried reader', to help readers wishing to develop, as efficiently as possible, a nontechnical appreciation of the Ricci flow program for 3-manifolds, i.e., the so-called 'fast track'. The book is suitable for geometers and others who are interested in the use of geometric analysis to study the structure of manifolds. "The Ricci Flow" was nominated for the 2005 Robert W. Hamilton Book Award, which is the highest honor of literary achievement given to published authors at the University of Texas at Austin.

Real and Stochastic Analysis

M. M. Rao
Real and Stochastic Analysis Book PDF

Author : M. M. Rao
Publisher : Springer Science & Business Media
Page : 411 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220541

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Real and Stochastic Analysis by M. M. Rao Pdf

As in the case of the two previous volumes published in 1986 and 1997, the purpose of this monograph is to focus the interplay between real (functional) analysis and stochastic analysis show their mutual benefits and advance the subjects. The presentation of each article, given as a chapter, is in a research-expository style covering the respective topics in depth. In fact, most of the details are included so that each work is essentially self contained and thus will be of use both for advanced graduate students and other researchers interested in the areas considered. Moreover, numerous new problems for future research are suggested in each chapter. The presented articles contain a substantial number of new results as well as unified and simplified accounts of previously known ones. A large part of the material cov ered is on stochastic differential equations on various structures, together with some applications. Although Brownian motion plays a key role, (semi-) martingale theory is important for a considerable extent. Moreover, noncommutative analysis and probabil ity have a prominent role in some chapters, with new ideas and results. A more detailed outline of each of the articles appears in the introduction and outline to assist readers in selecting and starting their work. All chapters have been reviewed.