The Geometry Of Total Curvature On Complete Open Surfaces
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The Geometry Of Total Curvature On Complete Open Surfaces
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Author : Katsuhiro Shiohama
language : en
Publisher: Cambridge University Press
Release Date : 2003-11-13
The Geometry Of Total Curvature On Complete Open Surfaces written by Katsuhiro Shiohama and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-13 with Mathematics categories.
This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.
Elements Of The Geometry And Topology Of Minimal Surfaces In Three Dimensional Space
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Author : A. T. Fomenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Elements Of The Geometry And Topology Of Minimal Surfaces In Three Dimensional Space written by A. T. Fomenko 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 2005 with Mathematics categories.
This book grew out of lectures presented to students of mathematics, physics, and mechanics by A. T. Fomenko at Moscow University, under the auspices of the Moscow Mathematical Society. The book describes modern and visual aspects of the theory of minimal, two-dimensional surfaces in three-dimensional space. The main topics covered are: topological properties of minimal surfaces, stable and unstable minimal films, classical examples, the Morse-Smale index of minimal two-surfaces in Euclidean space, and minimal films in Lobachevskian space. Requiring only a standard first-year calculus and elementary notions of geometry, this book brings the reader rapidly into this fascinating branch of modern geometry.
Handbook Of Differential Geometry Volume 1
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Author : F.J.E. Dillen
language : en
Publisher: Elsevier
Release Date : 1999-12-16
Handbook Of Differential Geometry Volume 1 written by F.J.E. Dillen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-16 with Mathematics categories.
In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.
Differential Geometry And Related Topics Proceedings Of The International Conference On Modern Mathematics And The International Symposium On Differential Geometry
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Author : Chaohao Gu
language : en
Publisher: World Scientific
Release Date : 2002-12-12
Differential Geometry And Related Topics Proceedings Of The International Conference On Modern Mathematics And The International Symposium On Differential Geometry written by Chaohao Gu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-12 with Mathematics categories.
The International Conference on Modern Mathematics and the International Symposium on Differential Geometry, in honor of Professor Su Buchin on the centenary of his birth, were held in September 2001 at Fudan University, Shanghai, China. Around 100 mathematicians from China, France, Japan, Singapore and the United States participated.The proceedings cover a broad spectrum of advanced topics in mathematics, especially in differential geometry, such as some problems of common interest in harmonic maps, submanifolds, the Yang-Mills field and the geometric theory of solitons.
Geometry Of Manifolds
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Author : K. Shiohama
language : en
Publisher: Elsevier
Release Date : 1989-10-04
Geometry Of Manifolds written by K. Shiohama and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-10-04 with Mathematics categories.
This volume contains the papers presented at a symposium on differential geometry at Shinshu University in July of 1988. Carefully reviewed by a panel of experts, the papers pertain to the following areas of research: dynamical systems, geometry of submanifolds and tensor geometry, lie sphere geometry, Riemannian geometry, Yang-Mills Connections, and geometry of the Laplace operator.
Mean Curvature Flow And Isoperimetric Inequalities
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Author : Manuel Ritoré
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-01
Mean Curvature Flow And Isoperimetric Inequalities written by Manuel Ritoré 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 2010-01-01 with Mathematics categories.
Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.
Curvature And Topology Of Riemannian Manifolds
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Author : Katsuhiro Shiohama
language : en
Publisher: Springer
Release Date : 2006-11-14
Curvature And Topology Of Riemannian Manifolds written by Katsuhiro Shiohama and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Behavior Of Distant Maximal Geodesics In Finitely Connected Complete 2 Dimensional Riemannian Manifolds
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Author : Takashi Shioya
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Behavior Of Distant Maximal Geodesics In Finitely Connected Complete 2 Dimensional Riemannian Manifolds written by Takashi Shioya 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 1994 with Mathematics categories.
This monograph studies the topological shapes of geodesics outside a large compact set in a finitely connected, complete, and noncompact surface admitting total curvature. When the surface is homeomorphic to a plane, all such geodesics behave like those of a flat cone. In particular, the rotation numbers of the geodesics are controlled by the total curvature. Accessible to beginners in differential geometry, but also of interest to specialists, this monograph features many illustrations that enhance understanding of the main ideas.
Symplectic Geometry
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Author : Helmut Hofer
language : en
Publisher: Springer Nature
Release Date : 2022-12-05
Symplectic Geometry written by Helmut Hofer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-05 with Mathematics categories.
Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Poincar Duality Algebras Macaulay S Dual Systems And Steenrod Operations
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Author : Dagmar M. Meyer
language : en
Publisher: Cambridge University Press
Release Date : 2005-08-18
Poincar Duality Algebras Macaulay S Dual Systems And Steenrod Operations written by Dagmar M. Meyer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-18 with Mathematics categories.
A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology.