Geometric Flows On Manifolds With Circle Action PDF Download
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Author | : Jarrod L. Pickens |
Publisher | : |
Total Pages | : 258 |
Release | : 2010 |
Genre | : |
ISBN | : 9781124332451 |
Download Geometric Flows on Manifolds with Circle Action Book in PDF, ePub and Kindle
We study the Ricci flow and cross curvature flow of a class of warped product metrics which are suitable for studying these flows on manifolds which admit a circle action, possibly with fixed points. This includes studying geometric flows on manifolds with boundary and discussing the necessary boundary conditions one must impose to obtain a well-defined flow. We derive the induced flows on the orbit space and study mixed boundary value problems of systems corresponding to the Ricci and cross curvature flows which are suitable for our situation. This involves studying the Ricci flow and cross curvature flow of a metric which is degenerate on the boundary of a manifold. We prove short time existence of solutions for these systems with certain assumptions made about the form of the warping function and metric on the orbit space in terms of parallel geodesic coordinates. We then study the evolution of various geometric quantities of interest along with evolution equations involving the warping function. We also derive the evolution of the first and second fundamental forms under these flows which are useful in studying these and other boundary value problems. We calculate certain quantities related to the curvature and cross curvature at the boundary of the manifold which may be used to study long time existence of solutions with additional conditions made on the warping functions and metric on the orbit space.
Author | : Huai-Dong Cao |
Publisher | : |
Total Pages | : 368 |
Release | : 2008 |
Genre | : Geometry, Differential |
ISBN | : |
Download Geometric Flows Book in PDF, ePub and Kindle
Author | : Igor Nikolaev |
Publisher | : Springer |
Total Pages | : 305 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 354048759X |
Download Flows on 2-dimensional Manifolds Book in PDF, ePub and Kindle
Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality. This book is a state-of-the-art account, covering classical and new results. The volume comprises Poincaré-Bendixson, local and Morse-Smale theories, as well as a carefully written chapter on the invariants of surface flows. Of particular interest are chapters on the Anosov-Weil problem, C*-algebras and non-compact surfaces. The book invites graduate students and non-specialists to a fascinating realm of research. It is a valuable source of reference to the specialists.
Author | : Danny Calegari |
Publisher | : Oxford University Press on Demand |
Total Pages | : 378 |
Release | : 2007-05-17 |
Genre | : Mathematics |
ISBN | : 0198570082 |
Download Foliations and the Geometry of 3-Manifolds Book in PDF, ePub and Kindle
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 | : Yael Karshon |
Publisher | : American Mathematical Soc. |
Total Pages | : 87 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 0821811819 |
Download Periodic Hamiltonian Flows on Four Dimensional Manifolds Book in PDF, ePub and Kindle
This book is intended for graduate students and research mathematicians interested in global analysis, analysis on manifolds, and symplectic geometry.
Author | : Owen Dearricott |
Publisher | : Springer |
Total Pages | : 196 |
Release | : 2014-08-05 |
Genre | : Mathematics |
ISBN | : 9783319063720 |
Download Geometry of Manifolds with Non-negative Sectional Curvature Book in PDF, ePub and Kindle
Providing an up-to-date overview of the geometry of manifolds with non-negative sectional curvature, this volume gives a detailed account of the most recent research in the area. The lectures cover a wide range of topics such as general isometric group actions, circle actions on positively curved four manifolds, cohomogeneity one actions on Alexandrov spaces, isometric torus actions on Riemannian manifolds of maximal symmetry rank, n-Sasakian manifolds, isoparametric hypersurfaces in spheres, contact CR and CR submanifolds, Riemannian submersions and the Hopf conjecture with symmetry. Also included is an introduction to the theory of exterior differential systems.
Author | : Jefferson Taft |
Publisher | : |
Total Pages | : 164 |
Release | : 2010 |
Genre | : |
ISBN | : |
Download Intrinsic Geometric Flows on Manifolds of Revolution Book in PDF, ePub and Kindle
An intrinsic geometric flow is an evolution of a Riemannian metric by a two-tensor. An extrinsic geometric flow is an evolution of an immersion of a manifold into Euclidean space. An extrinsic flow induces an evolution of a metric because any immersed manifold inherits a Riemannian metric from Euclidean space. In this paper we discuss the inverse problem of specifying an evolution of a metric and then seeking an extrinsic geometric flow which induces the given metric evolution. We limit our discussion to the case of manifolds that are rotationally symmetric and embeddable with codimension one. In this case, we reduce an intrinsic geometric flow to a plane curve evolution. In the specific cases we study, we are able to further simplify the evolution to an evolution of a function of one variable. We provide soliton equations and give proofs that some soliton metrics exist.
Author | : Danny Calegari |
Publisher | : Clarendon Press |
Total Pages | : 384 |
Release | : 2007-05-17 |
Genre | : Mathematics |
ISBN | : 0191524638 |
Download Foliations and the Geometry of 3-Manifolds Book in PDF, ePub and Kindle
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 in 1-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 | : Gerhard Huisken |
Publisher | : |
Total Pages | : 0 |
Release | : 2007 |
Genre | : |
ISBN | : |
Download Geometric Flows and 3-manifolds Book in PDF, ePub and Kindle
Author | : Bennett Chow |
Publisher | : American Mathematical Soc. |
Total Pages | : 790 |
Release | : 2020-05-14 |
Genre | : Education |
ISBN | : 147045596X |
Download Extrinsic Geometric Flows Book in PDF, ePub and Kindle
Extrinsic geometric flows are characterized by a submanifold evolving in an ambient space with velocity determined by its extrinsic curvature. The goal of this book is to give an extensive introduction to a few of the most prominent extrinsic flows, namely, the curve shortening flow, the mean curvature flow, the Gauß curvature flow, the inverse-mean curvature flow, and fully nonlinear flows of mean curvature and inverse-mean curvature type. The authors highlight techniques and behaviors that frequently arise in the study of these (and other) flows. To illustrate the broad applicability of the techniques developed, they also consider general classes of fully nonlinear curvature flows. The book is written at the level of a graduate student who has had a basic course in differential geometry and has some familiarity with partial differential equations. It is intended also to be useful as a reference for specialists. In general, the authors provide detailed proofs, although for some more specialized results they may only present the main ideas; in such cases, they provide references for complete proofs. A brief survey of additional topics, with extensive references, can be found in the notes and commentary at the end of each chapter.