Riemannian Geometry and Geometric Analysis (Universitext)

Book Description

This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. Besides several smaller additions, reorganizations, corrections, and a systematic bibliography, the main new features of the 4th edition are a systematic introduction to Kähler geometry and the presentation of additional techniques from geometric analysis.

From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry, e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. [..] The book is made more interesting by the perspectives in various sections." Math. Reviews

Customer Reviews:

maths background for General Relativity and QFT.......2007-01-11

For theoretical physicists, especially those studying Einstein's Theory of General Relativity, Or if your subject is quantum field theory. Jost's book is good preparation. He offers an in-depth teaching of Riemannian geometry. So ideas like covariant and contravariant derivatives on a manifold take on elegant meaning.

Note that General Relativity does not get an explicit mention. However, a typical physics GR course might often not have time to give a good discussion of the underlying maths. And standard GR texts, like Misner, Thorne and Wheeler or Weinberg, also tend to have very abbreviated explanations of the maths. So Jost's book is useful for those of you inclined to look further.

The length of the book means it's probably too long for a standard 1 term or semester course, if the intent is to entirely cover the book.

Intro to Riemannian Geom. and Geom. Analysis.......1999-07-02

Covers standard material on Reimannian Geometry. In addition: variational problems from QFT. Spin geometry and Dirac operators are explained in detail.

Geometric Partial Differential Equations and Image Analysis

Average customer rating:

Sapiro is smart!
Not really a good book

Geometric Partial Differential Equations and Image Analysis
Guillermo Sapiro
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

General | Graphic Design | Computers & Internet | Subjects | Books

Look Inside Computer Books | Trip | Specialty Stores | Books

All Deals | Blowout Books | Stores | Books

Computers & Internet | Blowout Books | Stores | Books

Science | Blowout Books | Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Computers & Internet | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

ASIN: 0521685079

Book Description

This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. It brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are achieved with the techniques described. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. The volume provides information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.

Customer Reviews:

Sapiro is smart!.......2003-02-20

Too bad Minnesota is so cold. Maybe we can buy him some gloves
and get another good book out him...

Not really a good book.......2002-03-16

well, I bought this book to learn image analysis using pde and
this book is not what I expected and unfortuanetly I ended up paying lots of money for it. The only use it has had so far is for me to know a topic's name and look for the mathematical definitions and implementation methods online. Most of the times, it is not clear what it's talking about, does not include real clarifying examples, it jumps from one kind of notation to another kind in the middle of explanation and the math at times is not clear and well written. Definitely not what you would expect from a book which invloves many fomulas/theories and proofs.

Geometric Inequalities (Grundlehren der mathematischen Wissenschaften, Vol. 285) (Grundlehren der mathematischen Wissenschaften)

Average customer rating:

Geometric Inequalities (Grundlehren der mathematischen Wissenschaften, Vol. 285) (Grundlehren der mathematischen Wissenschaften)
Yurii D. Burago , and Viktor A. Zalgaller
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

All Amazon Upgrade | Amazon Upgrade | Stores | Books

Professional & Technical | Amazon Upgrade | Stores | Books

Science | Amazon Upgrade | Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 3540136150

Geometric Mechanics on Riemannian Manifolds: Applications to Partial Differential Equations (Applied and Numerical Harmonic Analysis)

Average customer rating:

Geometric Mechanics on Riemannian Manifolds: Applications to Partial Differential Equations (Applied and Numerical Harmonic Analysis)
Ovidiu Calin , and Der-Chen Chang
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

All Amazon Upgrade | Amazon Upgrade | Stores | Books

Professional & Technical | Amazon Upgrade | Stores | Books

Science | Amazon Upgrade | Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

ASIN: 0817643540

Book Description

Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrödinger's, Einstein's and Newton's equations. Historically, problems in these areas were approached using the Fourier transform or path integrals, although in some cases (e.g., the case of quartic oscillators) these methods do not work. New geometric methods are introduced in the work that have the advantage of providing quantitative or at least qualitative descriptions of operators, many of which cannot be treated by other methods. And, conservation laws of the Euler–Lagrange equations are employed to solve the equations of motion qualitatively when quantitative analysis is not possible.

Main topics include: Lagrangian formalism on Riemannian manifolds; energy momentum tensor and conservation laws; Hamiltonian formalism; Hamilton–Jacobi theory; harmonic functions, maps, and geodesics; fundamental solutions for heat operators with potential; and a variational approach to mechanical curves. The text is enriched with good examples and exercises at the end of every chapter.

Geometric Mechanics on Riemannian Manifolds is a fine text for a course or seminar directed at graduate and advanced undergraduate students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics. It is also an ideal resource for pure and applied mathematicians and theoretical physicists working in these areas.

Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives (Cambridge Tracts in Mathematics)

Average customer rating:

Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives (Cambridge Tracts in Mathematics)
Isaac Chavel
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

General | Medicine | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Medicine | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 0521802679

Book Description

This introduction treats the classical isoperimetric inequality in Euclidean space and contrasting rough inequalities in noncompact Riemannian manifolds. In Euclidean space the emphasis is on a most general form of the inequality sufficiently precise to characterize the case of equality, and in Riemannian manifolds the emphasis is on those qualitiative features of the inequality that provide insight into the coarse geometry at infinity of Riemannian manifolds. The treatment in Euclidean space features a number of proofs of the classical inequality in increasing generality, providing in the process a transition from the methods of classical differential geometry to those of modern geometric measure theory; and the treatment in Riemannian manifolds features discretization techniques, and applications to upper bounds of large time heat diffusion in Riemannian manifolds. The result is an introduction to the rich tapestry of ideas and techniques of isoperimetric inequalities, a subject that has its beginnings in classical antiquity and which continues to inspire fresh ideas in geometry and analysis to this very day--and beyond!

The Geometry of Domains in Space (Birkhäuser Advanced Texts / Basler Lehrbücher)

Average customer rating:

The Geometry of Domains in Space

The Geometry of Domains in Space (Birkhäuser Advanced Texts / Basler Lehrbücher)
Steven G. Krantz , and Harold R. Parks
Manufacturer: Birkhauser
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

Mathematical Physics | Physics | Science | Subjects | Books

All Amazon Upgrade | Amazon Upgrade | Stores | Books

Professional & Technical | Amazon Upgrade | Stores | Books

Science | Amazon Upgrade | Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 0817640975

Book Description

Traditionally, analysis on Euclidean space is based on the study of the classical groups that act on the space. The classical treatises focus on rotations, dilations, and especially translations; all of these tools and techniques have shaped the way in which classical analysis on Euclidean space has developed.

On the other hand, a modern analytical treatment, such as the one presented here, often focuses on domains in space. A domain is the natural venue for various problems arising from physics, as well as the natural setting for the study of boundary value problems. Instead of considering group actions (inappropriate since a typical domain has on natural symmetries), one considers properties that arise from the intrinsic geometry of the domain and from the geometry of the boundary as a codimension one manifold in space.

Contributing to part of the new "toolkit" that should be at hand for every analyst, the authors cover a wide array of topics: imbedded manifolds, curvature, positive reach, Sard's theorem, Sobolev spaces, the isoperimetric inequality, Weyl's theorem, covering theorems, convex functions, and Stokes's theorem in all of its many formulations, to name just several. All geometric ideas are treated in a self-contained manner.

This comprehensive treatment of domains (in space) emphasizes the growing interaction between analysis and geometry. Geometric analysis, as it is known, is currently an important area of study for both pure and applied mathematicians, physicists, and engineers. Aimed at graduate students of the field, this monograph will be useful in the classroom or as a resource for self-study. The prerequisites are minimal; a good understanding of multivariate calculus and linear algebra will suffice for most purposes.

Customer Reviews:

The Geometry of Domains in Space.......2001-05-08

This book answers many puzzels of mine. I tried hard to read H. Federer's famous book , " geometric Measure Theory", and never finished reading it. Now I find Krantz and Parks' book more accessible and geometrical. Every mathematician working on geometrical analysis and partial differential equations will benefit from this book.

Riemannian Geometry (Graduate Texts in Mathematics)

Average customer rating:

Riemannian Geometry (Graduate Texts in Mathematics)
Peter Petersen
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

All Amazon Upgrade | Amazon Upgrade | Stores | Books

Professional & Technical | Amazon Upgrade | Stores | Books

Science | Amazon Upgrade | Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

ASIN: 0387982124

Book Description

This book is intended for a one year course in Riemannian Geometry. It will serve as a single source, introducing students to the important techniques and theorems while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian Geometry. Instead of variational techniques, the author uses a unique approach emphasizing distance functions and special coordinate systems. He also uses standard calculus with some techniques from differential equations, instead of variational calculus, thereby providing a more elementary route for students. Many of the chapters contain material typically found in specialized texts and never before published together in one source. Key sections include noteworthy coverage of: geodesic geometry, Bochner technique, symmetric spaces, holonomy, comparison theory for both Ricci and sectional curvature, and convergence theory. This volume is one of the few published works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory as well as presenting the most up-to-date research including sections on convergence and compactness of families of manifolds. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stoke's theorem. Scattered throughout the text is a variety of exercises which will help to motivate readers to deepen their understanding of the subject.

The Ab Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems (Memoirs of the American Mathematical Society)

Average customer rating:

The Ab Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems (Memoirs of the American Mathematical Society)
Olivier Druet , and Emmanuel Hebey
Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Almgren's Big Regularity Paper: Q-Valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-Minimizing Rectifiable Currents Up to Codimension ... Scientific Monograph Series in Mathematics)

Average customer rating:

Review of Almgren's big regularity paper

Almgren's Big Regularity Paper: Q-Valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-Minimizing Rectifiable Currents Up to Codimension ... Scientific Monograph Series in Mathematics)
Frederick J., Jr. Almgren
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 9810241089

Book Description

Fred Almgren exploited the excess method for proving regularity theorems in the calculus of variations. His techniques yielded Hölder continuous differentiability except for a small closed singular set. In the sixties and seventies Almgren refined and generalized his methods. Between 1974 and 1984 he wrote a 1,700-page proof that was his most ambitious development of his ground-breaking ideas. Originally, this monograph was available only as a three-volume work of limited circulation. The entire text is faithfully reproduced here.

This book gives a complete proof of the interior regularity of an area-minimizing rectifiable current up to Hausdorff codimension 2. The argument uses the theory of Q-valued functions, which is developed in detail. For example, this work shows how first variation estimates from squash and squeeze deformations yield a monotonicity theorem for the normalized frequency of oscillation of a Q-valued function that minimizes a generalized Dirichlet integral. The principal features of the book include an extension theorem analogous to Kirszbraun's theorem and theorems on the approximation in mass of nearly flat mass-minimizing rectifiable currents by graphs and images of Lipschitz Q-valued functions.

Customer Reviews:

Review of Almgren's big regularity paper.......2000-10-14

The publication of the Tex formatted version of Almgren's famous big regularity paper makes the original three-volume, 1700 page paper much easier to read. Especially, since Almgren developed the whole new machinery, it takes time for the beginning readers to become familiar with the terminology and to consult essential materials in the Appendix. Readers who have suffered reading the original three hand typed ``telephone books'' will appreciate this all-in-one book.

Book Description

The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.

Books:

Books Index

Books Home

Recommended Books