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Author : Dong-Pyo Chi
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.3/5 (91 download)
Download or read book Gromov-Hausdorff Topology and Its Applications to Riemannian Manifolds written by Dong-Pyo Chi and published by . This book was released on 1998 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mikhail Gromov
Publisher : Springer Science & Business Media
ISBN 13 : 9780817638986
Total Pages : 612 pages
Book Rating : 4.6/5 (389 download)
Download or read book Metric Structures for Riemannian and Non-Riemannian Spaces written by Mikhail Gromov and published by Springer Science & Business Media. This book was released on 2001-04-20 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.
Author : Filippo Cerocchi
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (992 download)
Download or read book Dynamical and Spectral Applications of Gromov-Hausdorff Theory written by Filippo Cerocchi and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Ph.D. Thesis is divided into two parts. In the first part we present the barycenter method, a technique which has been introduced by G. Besson, G. Courtois and S. Gallot in 1995, in order to solve the Minimal Entropy conjecture. In Chapter 1 we are interested in the more recent developments of this method, more precisely in the recent extension of the method to the case of manifolds having sectional curvature of variable sign. In Chapters 2 and 3 we shall present some new results whose proofs make use of the barycenter method. The Conjugacy Rigidity problem is the theme of Chapter 2. First we show a general result which provide a comparison between the large scale geometry of the Riemannian universal coverings of two compact manifolds whose geodesic flows are conjugates. Then we shall show how we can apply the latter result and the barycenter method in curvature of variable sign in order to give a new proof of the conjugacy rigidity of flat manifolds. In Chapter 3 we shall give a proof of a spectra comparison theorem for a compact Riemannian manifold which admits a Gromov-Hausdorff-approximation of non zero absolute degree on a fixed compact manifold (X,g') and which has volume almost smaller than the one of the reference manifold. The proof relies on the barycenter method in curvature of variable sign and on iterated Sobolev inequalities. We underline that it is an approximation result (and not just a convergence result) and that no curvature assumptions are made or inferred on (Y,g). The second part of the Thesis consists of a single chapter. In this chapter we prove a Margulis Lemma without curvature assumptions for Riemannian manifolds having decomposable 2-torsionless fundamental group. We shall give also a proof of a universal lower bound for the homotopy systole of compact Riemannian manifolds having bounded volume entropy and diameter, and decomposable torsionless fundamental group. As a consequence of the latter result we shall deduce a Precompactness and Finiteness theorem and a Volume estimate without curvature assumptions.
Author : Old?ich Kowalski
Publisher : World Scientific
ISBN 13 : 9812790608
Total Pages : 732 pages
Book Rating : 4.8/5 (127 download)
Download or read book Differential Geometry and Its Applications written by Old?ich Kowalski and published by World Scientific. This book was released on 2008 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.The book covers recent developments and the latest results in the following fields: Riemannian geometry, connections, jets, differential invariants, the calculus of variations on manifolds, differential equations, Finsler structures, and geometric methods in physics. It is also a celebration of the 300th anniversary of the birth of one of the greatest mathematicians, Leonhard Euler, and includes the Euler lecture ?Leonhard Euler ? 300 years on? by R Wilson. Notable contributors include J F Cari¤ena, M Castrill¢n L¢pez, J Erichhorn, J-H Eschenburg, I Kol ?, A P Kopylov, J Korba?, O Kowalski, B Kruglikov, D Krupka, O Krupkov , R Landre, Haizhong Li, S Maeda, M A Malakhaltsev, O I Mokhov, J Mu¤oz Masqu, S Preston, V Rovenski, D J Saunders, M Sekizawa, J Slov k, J Szilasi, L Tam ssy, P Walczak, and others.
Author : Gerardo Arizmendi Echegaray
Publisher : Springer Nature
ISBN 13 : 3030992985
Total Pages : 119 pages
Book Rating : 4.0/5 (39 download)
Download or read book Recent Advances in Alexandrov Geometry written by Gerardo Arizmendi Echegaray and published by Springer Nature. This book was released on 2022-10-27 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to various aspects of Alexandrov Geometry for those wishing to get a detailed picture of the advances in the field. It contains enhanced versions of the lecture notes of the two mini-courses plus those of one research talk given at CIMAT. Peter Petersen’s part aims at presenting various rigidity results about Alexandrov spaces in a way that facilitates the understanding by a larger audience of geometers of some of the current research in the subject. They contain a brief overview of the fundamental aspects of the theory of Alexandrov spaces with lower curvature bounds, as well as the aforementioned rigidity results with complete proofs. The text from Fernando Galaz-García’s minicourse was completed in collaboration with Jesús Nuñez-Zimbrón. It presents an up-to-date and panoramic view of the topology and geometry of 3-dimensional Alexandrov spaces, including the classification of positively and non-negatively curved spaces and the geometrization theorem. They also present Lie group actions and their topological and equivariant classifications as well as a brief account of results on collapsing Alexandrov spaces. Jesús Nuñez-Zimbrón’s contribution surveys two recent developments in the understanding of the topological and geometric rigidity of singular spaces with curvature bounded below.
Author : Jeff Cheeger
Publisher : Springer
ISBN 13 : 3540466517
Total Pages : 204 pages
Book Rating : 4.5/5 (44 download)
Download or read book Geometric Topology: Recent Developments written by Jeff Cheeger and published by Springer. This book was released on 2006-11-17 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Topology can be defined to be the investigation of global properties of a further structure (e.g. differentiable, Riemannian, complex,algebraic etc.) one can impose on a topological manifold. At the C.I.M.E. session in Montecatini, in 1990, three courses of lectures were given onrecent developments in this subject which is nowadays emerging as one of themost fascinating and promising fields of contemporary mathematics. The notesof these courses are collected in this volume and can be described as: 1) the geometry and the rigidity of discrete subgroups in Lie groups especially in the case of lattices in semi-simple groups; 2) the study of the critical points of the distance function and its appication to the understanding of the topology of Riemannian manifolds; 3) the theory of moduli space of instantons as a tool for studying the geometry of low-dimensional manifolds. CONTENTS: J. Cheeger: Critical Points of Distance Functions and Applications to Geometry.- M. Gromov, P. Pansu, Rigidity of Lattices: An Introduction.- Chr. Okonek: Instanton Invariants and Algebraic Surfaces.
Author : Demeter Krupka
Publisher : World Scientific
ISBN 13 : 9814471941
Total Pages : 732 pages
Book Rating : 4.8/5 (144 download)
Download or read book Differential Geometry And Its Applications - Proceedings Of The 10th International Conference On Dga2007 written by Demeter Krupka and published by World Scientific. This book was released on 2008-07-14 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.The book covers recent developments and the latest results in the following fields: Riemannian geometry, connections, jets, differential invariants, the calculus of variations on manifolds, differential equations, Finsler structures, and geometric methods in physics. It is also a celebration of the 300th anniversary of the birth of one of the greatest mathematicians, Leonhard Euler, and includes the Euler lecture “Leonhard Euler — 300 years on” by R Wilson. Notable contributors include J F Cariñena, M Castrillón López, J Erichhorn, J-H Eschenburg, I Kolář, A P Kopylov, J Korbaš, O Kowalski, B Kruglikov, D Krupka, O Krupková, R Léandre, Haizhong Li, S Maeda, M A Malakhaltsev, O I Mokhov, J Muñoz Masqué, S Preston, V Rovenski, D J Saunders, M Sekizawa, J Slovák, J Szilasi, L Tamássy, P Walczak, and others.
Author : Szymon M. Walczak
Publisher : Springer
ISBN 13 : 3319575171
Total Pages : 63 pages
Book Rating : 4.3/5 (195 download)
Download or read book Metric Diffusion Along Foliations written by Szymon M. Walczak and published by Springer. This book was released on 2017-05-16 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: Up-to-date research in metric diffusion along compact foliations is presented in this book. Beginning with fundamentals from the optimal transportation theory and the theory of foliations; this book moves on to cover Wasserstein distance, Kantorovich Duality Theorem, and the metrization of the weak topology by the Wasserstein distance. Metric diffusion is defined, the topology of the metric space is studied and the limits of diffused metrics along compact foliations are discussed. Essentials on foliations, holonomy, heat diffusion, and compact foliations are detailed and vital technical lemmas are proved to aide understanding. Graduate students and researchers in geometry, topology and dynamics of foliations and laminations will find this supplement useful as it presents facts about the metric diffusion along non-compact foliation and provides a full description of the limit for metrics diffused along foliation with at least one compact leaf on the two dimensions.
Author : Jihoon Lee
Publisher : Springer Nature
ISBN 13 : 3031120310
Total Pages : 169 pages
Book Rating : 4.0/5 (311 download)
Download or read book Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs written by Jihoon Lee and published by Springer Nature. This book was released on 2022-10-30 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents new insights into the perturbation theory of dynamical systems based on the Gromov-Hausdorff distance. In the first part, the authors introduce the notion of Gromov-Hausdorff distance between compact metric spaces, along with the corresponding distance for continuous maps, flows, and group actions on these spaces. They also focus on the stability of certain dynamical objects like shifts, global attractors, and inertial manifolds. Applications to dissipative PDEs, such as the reaction-diffusion and Chafee-Infante equations, are explored in the second part. This text will be of interest to graduates students and researchers working in the areas of topological dynamics and PDEs.
Author : Werner Gähler
Publisher : Wiley-VCH
ISBN 13 :
Total Pages : 328 pages
Book Rating : 4.F/5 ( download)
Download or read book Recent Developments of General Topology and Its Applications written by Werner Gähler and published by Wiley-VCH. This book was released on 1992-10-23 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the main part of the lectures contributed to the conference. They reflect the new trends of development in general topology.
Author : Stefano Bianchini
Publisher : Springer Science & Business Media
ISBN 13 : 3642217184
Total Pages : 237 pages
Book Rating : 4.6/5 (422 download)
Download or read book Nonlinear PDE’s and Applications written by Stefano Bianchini and published by Springer Science & Business Media. This book was released on 2011-07-30 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects the notes of the CIME course "Nonlinear PDE’s and applications" held in Cetraro (Italy) on June 23–28, 2008. It consists of four series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), and Cédric Villani (Ecole Normale Superieure de Lyon). They presented a broad overview of far-reaching findings and exciting new developments concerning, in particular, optimal transport theory, nonlinear evolution equations, functional inequalities, and differential geometry. A sampling of the main topics considered here includes optimal transport, Hamilton-Jacobi equations, Riemannian geometry, and their links with sharp geometric/functional inequalities, variational methods for studying nonlinear evolution equations and their scaling properties, and the metric/energetic theory of gradient flows and of rate-independent evolution problems. The book explores the fundamental connections between all of these topics and points to new research directions in contributions by leading experts in these fields.
Author : Stephen Keith
Publisher :
ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.3/5 (91 download)
Download or read book A Differentiable Structure for Metric Measure Spaces written by Stephen Keith and published by . This book was released on 2002 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard Montgomery
Publisher : American Mathematical Soc.
ISBN 13 : 0821841653
Total Pages : 282 pages
Book Rating : 4.8/5 (218 download)
Download or read book A Tour of Subriemannian Geometries, Their Geodesics and Applications written by Richard Montgomery and published by American Mathematical Soc.. This book was released on 2002 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subriemannian geometries can be viewed as limits of Riemannian geometries. They arise naturally in many areas of pure (algebra, geometry, analysis) and applied (mechanics, control theory, mathematical physics) mathematics, as well as in applications (e.g., robotics). This book is devoted to the study of subriemannian geometries, their geodesics, and their applications. It starts with the simplest nontrivial example of a subriemannian geometry: the two-dimensional isoperimetric problem reformulated as a problem of finding subriemannian geodesics. Among topics discussed in other chapters of the first part of the book are an elementary exposition of Gromov's idea to use subriemannian geometry for proving a theorem in discrete group theory and Cartan's method of equivalence applied to the problem of understanding invariants of distributions. The second part of the book is devoted to applications of subriemannian geometry. In particular, the author describes in detail Berry's phase in quantum mechanics, the problem of a falling cat righting herself, that of a microorganism swimming, and a phase problem arising in the $N$-body problem. He shows that all these problems can be studied using the same underlying type of subriemannian geometry. The reader is assumed to have an introductory knowledge of differential geometry. This book that also has a chapter devoted to open problems can serve as a good introduction to this new, exciting area of mathematics.
Author : Michel Boileau
Publisher : Springer
ISBN 13 : 3319423517
Total Pages : 149 pages
Book Rating : 4.3/5 (194 download)
Download or read book Ricci Flow and Geometric Applications written by Michel Boileau and published by Springer. This book was released on 2016-09-09 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. The book’s four chapters are based on lectures given by leading researchers in the field of geometric analysis and low-dimensional geometry/topology, respectively offering an introduction to: the differentiable sphere theorem (G. Besson), the geometrization of 3-manifolds (M. Boileau), the singularities of 3-dimensional Ricci flows (C. Sinestrari), and Kähler–Ricci flow (G. Tian). The lectures will be particularly valuable to young researchers interested in differential manifolds.
Author : Bennett Chow
Publisher : American Mathematical Soc.
ISBN 13 : 0821846612
Total Pages : 542 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Ricci Flow: Techniques and Applications written by Bennett Chow and published by American Mathematical Soc.. This book was released on 2010-04-21 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects. The topics include Perelman's entropy functional, point picking methods, aspects of Perelman's theory of $\kappa$-solutions including the $\kappa$-gap theorem, compactness theorem and derivative estimates, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the appendices, we review metric and Riemannian geometry including the space of points at infinity and Sharafutdinov retraction for complete noncompact manifolds with nonnegative sectional curvature. As in the previous volumes, the authors have endeavored, as much as possible, to make the chapters independent of each other. The book makes advanced material accessible to graduate students and nonexperts. It includes a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors give the appropriate references so that the reader may further pursue the statements and proofs of the various results.
Author : F Thomas Farrell
Publisher : World Scientific
ISBN 13 : 9814487074
Total Pages : 510 pages
Book Rating : 4.8/5 (144 download)
Download or read book High-dimensional Manifold Topology - Proceedings Of The School written by F Thomas Farrell and published by World Scientific. This book was released on 2003-10-17 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: A Foliated Squeezing Theorem for Geometric Modules (A Bartels et al.)Equivariant Cellular Homology and Its Applications (B Chorny)Remarks on a Conjecture of Gromov and Lawson (W Dwyer et al.)Chain Complex Invariants for Group Actions (L E Jones)The Ore Condition, Affiliated Operators, and the Lamplighter Group (P A Linnell et al.)The Surgery Exact Sequence Revisited (E K Pedersen)K-theory for Proper Smooth Actions of Totally Disconnected Groups (J Sauer)Geometric Chain Homotopy Equivalences between Novikov Complexes (D Schütz)and other papers Readership: Graduate students and researchers in geometry and topology. Keywords:High-Dimensional Manifold Topology;Operator Algebras;K-Theory;L-Theory;Foliated Control Theory
Author :
Publisher : ScholarlyEditions
ISBN 13 : 1464964793
Total Pages : 995 pages
Book Rating : 4.4/5 (649 download)
Download or read book Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 995 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Operations, and Computational Mathematics and Geometry. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Operations, and Computational Mathematics and Geometry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
