Affine Flows on 3-Manifolds PDF Download
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Author: Shigenori Matsumoto
Publisher: American Mathematical Soc.
ISBN: 0821832573
Category : Mathematics
Languages : en
Pages : 106
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Book Description
Considers nonsingular flows on closed 3-manifolds which are transversely modeled on the real affine geometry of the plane. This book obtains classification results for three types of flows.
Author: Shigenori Matsumoto
Publisher: American Mathematical Soc.
ISBN: 0821832573
Category : Mathematics
Languages : en
Pages : 106
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Book Description
Considers nonsingular flows on closed 3-manifolds which are transversely modeled on the real affine geometry of the plane. This book obtains classification results for three types of flows.
Author: Danny Calegari
Publisher: Oxford University Press on Demand
ISBN: 0198570082
Category : Mathematics
Languages : en
Pages : 378
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Book Description
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Author:
Publisher: American Mathematical Soc.
ISBN: 0821839462
Category : Mathematics
Languages : en
Pages : 562
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Book Description
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.
![The Proceedings of the Conference[s] on Geometric Structures on Manifolds PDF](https://books.google.com/books/content/images/frontcover/AkHvAAAAMAAJ?fife=w80-h100)
Author: Suhyoung Choi
Publisher:
ISBN:
Category : Gauge fields (Physics)
Languages : en
Pages : 206
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Book Description
Author: Nicolau Corção Saldanha
Publisher: American Mathematical Soc.
ISBN: 0821846280
Category : Mathematics
Languages : en
Pages : 247
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Book Description
Presents the proceedings of the conference on Foliations, Geometry, and Topology, held August 6-10, 2007, in Rio de Janeiro, Brazil, in honor of the 70th birthday of Paul Schweitzer. The papers focus on the theory of foliations and related areas such as dynamical systems, group actions on low dimensional manifolds, and geometry of hypersurfaces.
Author: F. Bethuel
Publisher: Springer
ISBN: 3540488138
Category : Mathematics
Languages : en
Pages : 299
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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.
Author: Philippe Tondeur
Publisher: Birkhäuser
ISBN: 3034889143
Category : Mathematics
Languages : en
Pages : 308
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Book Description
The topics in this survey volume concern research done on the differential geom etry of foliations over the last few years. After a discussion of the basic concepts in the theory of foliations in the first four chapters, the subject is narrowed down to Riemannian foliations on closed manifolds beginning with Chapter 5. Following the discussion of the special case of flows in Chapter 6, Chapters 7 and 8 are de voted to Hodge theory for the transversal Laplacian and applications of the heat equation method to Riemannian foliations. Chapter 9 on Lie foliations is a prepa ration for the statement of Molino's Structure Theorem for Riemannian foliations in Chapter 10. Some aspects of the spectral theory for Riemannian foliations are discussed in Chapter 11. Connes' point of view of foliations as examples of non commutative spaces is briefly described in Chapter 12. Chapter 13 applies ideas of Riemannian foliation theory to an infinite-dimensional context. Aside from the list of references on Riemannian foliations (items on this list are referred to in the text by [ ]), we have included several appendices as follows. Appendix A is a list of books and surveys on particular aspects of foliations. Appendix B is a list of proceedings of conferences and symposia devoted partially or entirely to foliations. Appendix C is a bibliography on foliations, which attempts to be a reasonably complete list of papers and preprints on the subject of foliations up to 1995, and contains approximately 2500 titles.
Author: Frank Nielsen
Publisher: Springer
ISBN: 3642008267
Category : Computers
Languages : en
Pages : 397
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Book Description
This book features contributions from the LIX Fall Colloquium on the Emerging Trends in Visual Computing, ETVC 2008. Coverage includes information geometry and applications, computer graphics and vision, and medical imaging and computational anatomy.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 974
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Book Description
Author: Bennett Chow
Publisher: American Mathematical Soc.
ISBN: 0821849913
Category : Mathematics
Languages : en
Pages : 397
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Book Description
Ricci flow is a powerful technique using a heat-type equation to deform Riemannian metrics on manifolds to better metrics in the search for geometric decompositions. With the fourth part of their volume on techniques and applications of the theory, the authors discuss long-time solutions of the Ricci flow and related topics. In dimension 3, Perelman completed Hamilton's program to prove Thurston's geometrization conjecture. In higher dimensions the Ricci flow has remarkable properties, which indicates its usefulness to understand relations between the geometry and topology of manifolds. This book discusses recent developments on gradient Ricci solitons, which model the singularities developing under the Ricci flow. In the shrinking case there is a surprising rigidity which suggests the likelihood of a well-developed structure theory. A broader class of solutions is ancient solutions; the authors discuss the beautiful classification in dimension 2. In higher dimensions they consider both ancient and singular Type I solutions, which must have shrinking gradient Ricci soliton models. Next, Hamilton's theory of 3-dimensional nonsingular solutions is presented, following his original work. Historically, this theory initially connected the Ricci flow to the geometrization conjecture. From a dynamical point of view, one is interested in the stability of the Ricci flow. The authors discuss what is known about this basic problem. Finally, they consider the degenerate neckpinch singularity from both the numerical and theoretical perspectives. This book makes advanced material accessible to researchers and graduate students who are interested in the Ricci flow and geometric evolution equations and who have a knowledge of the fundamentals of the Ricci flow.
