Old And New Aspects In Spectral Geometry

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Old And New Aspects In Spectral Geometry

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Author : M. -E. Craioveanu
language : en
Publisher:
Release Date : 2014-01-15

Old And New Aspects In Spectral Geometry written by M. -E. Craioveanu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Old And New Aspects In Spectral Geometry

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Author : M.-E. Craioveanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Old And New Aspects In Spectral Geometry written by M.-E. Craioveanu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

It is known that to any Riemannian manifold (M, g ) , with or without boundary, one can associate certain fundamental objects. Among them are the Laplace-Beltrami opera tor and the Hodge-de Rham operators, which are natural [that is, they commute with the isometries of (M,g)], elliptic, self-adjoint second order differential operators acting on the space of real valued smooth functions on M and the spaces of smooth differential forms on M, respectively. If M is closed, the spectrum of each such operator is an infinite divergent sequence of real numbers, each eigenvalue being repeated according to its finite multiplicity. Spectral Geometry is concerned with the spectra of these operators, also the extent to which these spectra determine the geometry of (M, g) and the topology of M. This problem has been translated by several authors (most notably M. Kac). into the col loquial question "Can one hear the shape of a manifold?" because of its analogy with the wave equation. This terminology was inspired from earlier results of H. Weyl. It is known that the above spectra cannot completely determine either the geometry of (M , g) or the topology of M. For instance, there are examples of pairs of closed Riemannian manifolds with the same spectra corresponding to the Laplace-Beltrami operators, but which differ substantially in their geometry and which are even not homotopically equiva lent.

The Ricci Flow Techniques And Applications

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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 2007-04-11

The Ricci Flow Techniques And Applications written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-11 with Mathematics categories.

This book gives a presentation of topics in Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject. The authors have aimed at presenting technical material in a clear and detailed manner. In this volume, geometric aspects of the theory have been emphasized. The book presents the theory of Ricci solitons, Kahler-Ricci flow, compactness theorems, Perelman's entropy monotonicity and no local collapsing, Perelman's reduced distance function and applications to ancient solutions, and a primer of 3-manifold topology. Various technical aspects of Ricci flow have been explained in a clear and detailed manner. The authors have tried to make some advanced material accessible to graduate students and nonexperts. The book gives a rigorous introduction to Perelman's work and explains technical aspects of Ricci flow useful for singularity analysis. Throughout, there are appropriate references so that the reader may further pursue the statements and proofs of the various results.

Differential Geometry

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Author : Jes£s A. Alvarez L¢pez
language : en
Publisher: World Scientific
Release Date : 2009

Differential Geometry written by Jes£s A. Alvarez L¢pez and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

This volume contains research and expository papers on recent advances in foliations and Riemannian geometry. Some of the topics covered in this volume include: topology, geometry, dynamics and analysis of foliations, curvature, submanifold theory, Lie groups and harmonic maps.Among the contributions, readers may find an extensive survey on characteristic classes of Riemannian foliations offering also new results, an article showing the uniform simplicity of certain diffeomorphism groups, an exposition of convergences of contact structures to foliations from the point of view of Thurston's and Thurston?Bennequin's inequalities, a discussion about Fatou?Julia decompositions for foliations and a description of singular Riemannian foliations on spaces without conjugate points.Papers on submanifold theory focus on the existence of graphs with prescribed mean curvature and mean curvature flow for spacelike graphs, isometric and conformal deformations and detailed surveys on totally geodesic submanifolds in symmetric spaces, cohomogeneity one actions on hyperbolic spaces and rigidity of geodesic spheres in space forms. Geometric realizability of curvature tensors and curvature operators are also treated in this volume with special attention to the affine and the pseudo-Riemannian settings. Also, some contributions on biharmonic maps and submanifolds enrich the scope of this volume in providing an overview of different topics of current interest in differential geometry.

The Ricci Flow Techniques And Applications

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Author : Bennett Chow
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

The Ricci Flow Techniques And Applications written by Bennett Chow and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Global differential geometry categories.

Function Spaces And Partial Differential Equations

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Author : Ali Taheri
language : en
Publisher: Oxford University Press
Release Date : 2015-07-30

Function Spaces And Partial Differential Equations written by Ali Taheri and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-30 with Mathematics categories.

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Function Spaces And Partial Differential Equations

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Author : Ali Taheri
language : en
Publisher: Oxford Lecture Mathematics and
Release Date : 2015

Function Spaces And Partial Differential Equations written by Ali Taheri and has been published by Oxford Lecture Mathematics and this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Nonlinear Analysis

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Author : Panos M. Pardalos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-02

Nonlinear Analysis written by Panos M. Pardalos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-02 with Mathematics categories.

The volume will consist of about 40 articles written by some very influential mathematicians of our time and will expose the latest achievements in the broad area of nonlinear analysis and its various interdisciplinary applications.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2007

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

The Ricci Flow

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Author :
language : en
Publisher:
Release Date : 2007

The Ricci Flow written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Global differential geometry categories.