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Author : Robert Osserman
Publisher : American Mathematical Soc.
ISBN 13 : 0821814397
Total Pages : 333 pages
Book Rating : 4.8/5 (218 download)
Download or read book Geometry of the Laplace Operator written by Robert Osserman and published by American Mathematical Soc.. This book was released on 1980 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Osserman
Publisher : American Mathematical Soc.
ISBN 13 : 9780821867969
Total Pages : 340 pages
Book Rating : 4.8/5 (679 download)
Download or read book Geometry of the Laplace Operator written by Robert Osserman and published by American Mathematical Soc.. This book was released on 1980-12-31 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : American Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 323 pages
Book Rating : 4.:/5 (878 download)
Download or read book Geometry of the Laplace Operator written by American Mathematical Society and published by . This book was released on 1980 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Steven Rosenberg
Publisher : Cambridge University Press
ISBN 13 : 9780521468312
Total Pages : 190 pages
Book Rating : 4.4/5 (683 download)
Download or read book The Laplacian on a Riemannian Manifold written by Steven Rosenberg and published by Cambridge University Press. This book was released on 1997-01-09 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
Author : Udo Simon
Publisher :
ISBN 13 :
Total Pages : 72 pages
Book Rating : 4.:/5 (255 download)
Download or read book Geometry of the Laplace operator written by Udo Simon and published by . This book was released on 1980 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Osserman
Publisher :
ISBN 13 :
Total Pages : 323 pages
Book Rating : 4.:/5 (989 download)
Download or read book Geometry of the Laplace Operator written by Robert Osserman and published by . This book was released on 1980 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bennett Chow
Publisher : American Mathematical Society, Science Press
ISBN 13 : 1470473690
Total Pages : 648 pages
Book Rating : 4.4/5 (74 download)
Download or read book Hamilton’s Ricci Flow written by Bennett Chow and published by American Mathematical Society, Science Press. This book was released on 2023-07-13 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty. The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible. Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions. A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincaré conjecture and Thurston's geometrization conjecture.
Author : Peter Buser
Publisher : Springer Science & Business Media
ISBN 13 : 0817649921
Total Pages : 473 pages
Book Rating : 4.8/5 (176 download)
Download or read book Geometry and Spectra of Compact Riemann Surfaces written by Peter Buser and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature –1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.
Author : Robert Osserman
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (476 download)
Download or read book Geometry of the Laplace Operator written by Robert Osserman and published by . This book was released on 1980 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hajime Urakawa
Publisher : World Scientific
ISBN 13 : 9813109106
Total Pages : 310 pages
Book Rating : 4.8/5 (131 download)
Download or read book Spectral Geometry Of The Laplacian: Spectral Analysis And Differential Geometry Of The Laplacian written by Hajime Urakawa and published by World Scientific. This book was released on 2017-06-02 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is called the spectrum. We describe how the spectrum determines a Riemannian manifold. The continuity of the eigenvalue of the Laplacian, Cheeger and Yau's estimate of the first eigenvalue, the Lichnerowicz-Obata's theorem on the first eigenvalue, the Cheng's estimates of the kth eigenvalues, and Payne-Pólya-Weinberger's inequality of the Dirichlet eigenvalue of the Laplacian are also described. Then, the theorem of Colin de Verdière, that is, the spectrum determines the totality of all the lengths of closed geodesics is described. We give the V Guillemin and D Kazhdan's theorem which determines the Riemannian manifold of negative curvature.
Download or read book Proceedings of Symposia in Pure Mathematics written by and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pierre H. Berard
Publisher : Springer
ISBN 13 : 3540409580
Total Pages : 284 pages
Book Rating : 4.5/5 (44 download)
Download or read book Spectral Geometry written by Pierre H. Berard and published by Springer. This book was released on 2006-11-14 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Steve Zelditch
Publisher : American Mathematical Soc.
ISBN 13 : 1470410370
Total Pages : 410 pages
Book Rating : 4.4/5 (74 download)
Download or read book Eigenfunctions of the Laplacian on a Riemannian Manifold written by Steve Zelditch and published by American Mathematical Soc.. This book was released on 2017-12-12 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.
Author : Der-Chen Chang
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110642999
Total Pages : 266 pages
Book Rating : 4.1/5 (16 download)
Download or read book The Sub-Laplacian Operators of Some Model Domains written by Der-Chen Chang and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-08-01 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book studies sub-Laplacian operators on a family of model domains in C^{n+1}, which is a good point-wise model for a $CR$ manifold with non-degenerate Levi form. A considerable amount of study has been devoted to partial differential operators constructed from non-commuting vector fields, in which the non-commutativity plays an essential role in determining the regularity properties of the operators.
Author : Ivan Kolar
Publisher : Springer Science & Business Media
ISBN 13 : 3662029502
Total Pages : 440 pages
Book Rating : 4.6/5 (62 download)
Download or read book Natural Operations in Differential Geometry written by Ivan Kolar and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M.
Author : M.-E. Craioveanu
Publisher : Springer Science & Business Media
ISBN 13 : 940172475X
Total Pages : 447 pages
Book Rating : 4.4/5 (17 download)
Download or read book Old and New Aspects in Spectral Geometry written by M.-E. Craioveanu and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : H. Blaine Lawson
Publisher : Princeton University Press
ISBN 13 : 1400883911
Total Pages : 442 pages
Book Rating : 4.4/5 (8 download)
Download or read book Spin Geometry written by H. Blaine Lawson and published by Princeton University Press. This book was released on 2016-06-02 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds.
