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Ad Alexandrov Selected Works Intrinsic Geometry Of Convex Surfaces
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Book Synopsis A.D. Alexandrov by : S.S. Kutateladze
Download or read book A.D. Alexandrov written by S.S. Kutateladze and published by CRC Press. This book was released on 2005-07-25 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: A.D. Alexandrov is considered by many to be the father of intrinsic geometry, second only to Gauss in surface theory. That appraisal stems primarily from this masterpiece--now available in its entirely for the first time since its 1948 publication in Russian. Alexandrov's treatise begins with an outline of the basic concepts, definitions, and r
Book Synopsis A.D. Alexandrov, Selected Works: Intrinsic geometry of convex surfaces by : Aleksandr Danilovich Aleksandrov
Download or read book A.D. Alexandrov, Selected Works: Intrinsic geometry of convex surfaces written by Aleksandr Danilovich Aleksandrov and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A.D. Alexandrov by : S.S. Kutateladze
Download or read book A.D. Alexandrov written by S.S. Kutateladze and published by Chapman and Hall/CRC. This book was released on 2005-07-25 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: A.D. Alexandrov is considered by many to be the father of intrinsic geometry, second only to Gauss in surface theory. That appraisal stems primarily from this masterpiece--now available in its entirely for the first time since its 1948 publication in Russian. Alexandrov's treatise begins with an outline of the basic concepts, definitions, and results relevant to intrinsic geometry. It reviews the general theory, then presents the requisite general theorems on rectifiable curves and curves of minimum length. Proof of some of the general properties of the intrinsic metric of convex surfaces follows. The study then splits into two almost independent lines: further exploration of the intrinsic geometry of convex surfaces and proof of the existence of a surface with a given metric. The final chapter reviews the generalization of the whole theory to convex surfaces in the Lobachevskii space and in the spherical space, concluding with an outline of the theory of nonconvex surfaces. Alexandrov's work was both original and extremely influential. This book gave rise to studying surfaces "in the large," rejecting the limitations of smoothness, and reviving the style of Euclid. Progress in geometry in recent decades correlates with the resurrection of the synthetic methods of geometry and brings the ideas of Alexandrov once again into focus. This text is a classic that remains unsurpassed in its clarity and scope.
Book Synopsis A.D. Alexandrov by : S.S. Kutateladze
Download or read book A.D. Alexandrov written by S.S. Kutateladze and published by CRC Press. This book was released on 2005-07-25 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: A.D. Alexandrov is considered by many to be the father of intrinsic geometry. A two-volume set, A.D. Alexandrov Selected Works contains some of the most important papers by this renowned geometer. Volume 1 covers convex polyhedrons and closed surfaces, an elementary proof and extension of Minkowski's theorem, Riemannian geometry and a method for Dirichlet problems. Volume 2 covers general propositions on an intrinsic metric, angles and curvature, the existence of a convex polyhedron with prescribed metric, curves on convex surfaces, and the role of specific curvature. These monographs, published in English for the first time, will appeal to advanced students and researchers in mathematics and geometry.
Book Synopsis A.D. Alexandrov Selected Works, Part II by : S. S. Kutateladze
Download or read book A.D. Alexandrov Selected Works, Part II written by S. S. Kutateladze and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A.D. Alexandrov is considered by many to be the father of intrinsic geometry, second only to Gauss in surface theory. That appraisal stems primarily from this masterpiece--now available in its entirely for the first time since its 1948 publication in Russian. Alexandrov's treatise begins with an outline of the basic concepts, definitions, and results relevant to intrinsic geometry. It reviews the general theory, then presents the requisite general theorems on rectifiable curves and curves of minimum length. Proof of some of the general properties of the intrinsic metric of convex surfaces fo.
Book Synopsis A. D. Alexandrov Selected Works Part I by : Yu. G. Reshetnyak
Download or read book A. D. Alexandrov Selected Works Part I written by Yu. G. Reshetnyak and published by CRC Press. This book was released on 2002-02-21 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alexandr Danilovich Alexandrov has been called a giant of 20th-century mathematics. This volume contains some of the most important papers by this renowned geometer and hence, some of his most influential ideas. Alexandrov addressed a wide range of modern mathematical problems, and he did so with intelligence and elegance, solving some of the disci
Book Synopsis A. D. Alexandrov Selected Works by : Yu. G. Reshetnyak
Download or read book A. D. Alexandrov Selected Works written by Yu. G. Reshetnyak and published by CRC Press. This book was released on 2002-02-21 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alexandr Danilovich Alexandrov has been called a giant of 20th-century mathematics. This volume contains some of the most important papers by this renowned geometer and hence, some of his most influential ideas. Alexandrov addressed a wide range of modern mathematical problems, and he did so with intelligence and elegance, solving some of the discipline's most difficult and enduring challenges. He was the first to apply many of the tools and methods of the theory of real functions and functional analysis that are now current in geometry. The topics here include convex polyhedrons and closed surfaces, an elementary proof and extension of Minkowski's theorem, Riemannian geometry and a method for Dirichlet problems. This monograph, published in English for the first time, gives unparalleled access to a brilliant mind, and advanced students and researchers in applied mathematics and geometry will find it indispensable.
Book Synopsis A. D. Alexandrov Selected Works by : Yu G Reshetnyak
Download or read book A. D. Alexandrov Selected Works written by Yu G Reshetnyak and published by CRC Press. This book was released on 2019-08-30 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alexandr Danilovich Alexandrov has been called a giant of 20th-century mathematics. This volume contains some of the most important papers by this renowned geometer and hence, some of his most influential ideas. Alexandrov addressed a wide range of modern mathematical problems, and he did so with intelligence and elegance, solving some of the discipline's most difficult and enduring challenges. He was the first to apply many of the tools and methods of the theory of real functions and functional analysis that are now current in geometry. The topics here include convex polyhedrons and closed surfaces, an elementary proof and extension of Minkowski's theorem, Riemannian geometry and a method for Dirichlet problems. This monograph, published in English for the first time, gives unparalleled access to a brilliant mind, and advanced students and researchers in applied mathematics and geometry will find it indispensable.
Book Synopsis Reshaping Convex Polyhedra by : Joseph O’Rourke
Download or read book Reshaping Convex Polyhedra written by Joseph O’Rourke and published by Springer Nature. This book was released on with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Folding Algorithms by : Erik D. Demaine
Download or read book Geometric Folding Algorithms written by Erik D. Demaine and published by Cambridge University Press. This book was released on 2007-07-16 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.
Author :Victor Andreevich Toponogov Publisher :Springer Science & Business Media ISBN 13 :0817644024 Total Pages :215 pages Book Rating :4.8/5 (176 download)
Book Synopsis Differential Geometry of Curves and Surfaces by : Victor Andreevich Toponogov
Download or read book Differential Geometry of Curves and Surfaces written by Victor Andreevich Toponogov and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels
Book Synopsis Reshetnyak's Theory of Subharmonic Metrics by : François Fillastre
Download or read book Reshetnyak's Theory of Subharmonic Metrics written by François Fillastre and published by Springer Nature. This book was released on 2023-10-20 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite the fundamental role played by Reshetnyak's work in the theory of surfaces of bounded integral curvature, the proofs of his results were only available in his original articles, written in Russian and often hard to find. This situation used to be a serious problem for experts in the field. This book provides English translations of the full set of Reshetnyak's articles on the subject. Together with the companion articles, this book provides an accessible and comprehensive reference for the subject. In turn, this book should concern any researcher (confirmed or not) interested in, or active in, the field of bounded integral curvature surfaces, or more generally interested in surface geometry and geometric analysis. Due to the analytic nature of Reshetnyak's approach, it appears that his articles are very accessible for a modern audience, comparing to the works using a more synthetic approach. These articles of Reshetnyak concern more precisely the work carried by the author following the completion of his PhD thesis, under the supervision of A.D. Alexandrov. Over the period from the 1940’s to the 1960’s, the Leningrad School of Geometry, developed a theory of the metric geometry of surfaces, similar to the classical theory of Riemannian surfaces, but with lower regularity, allowing greater flexibility. Let us mention A.D. Alexandrov, Y.D. Burago and V.A. Zalgaller. The types of surfaces studied by this school are now known as surfaces of bounded curvature. Particular cases are that of surfaces with curvature bounded from above or below, the study of which gained special attention after the works of M. Gromov and G. Perelman. Nowadays, these concepts have been generalized to higher dimensions, to graphs, and so on, and the study of metrics of weak regularity remains an active and challenging field. Reshetnyak developed an alternative and analytic approach to surfaces of bounded integral curvature. The underlying idea is based on the theorem of Gauss which states that every Riemannian surface is locally conformal to Euclidean space. Reshetnyak thus studied generalized metrics which are locally conformal to the Euclidean metric with conformal factor given by the logarithm of the difference between two subharmonic functions on the plane. Reshetnyak's condition appears to provide the correct regularity required to generalize classical concepts such as measure of curvature, integral geodesic curvature for curves, and so on, and in turn, to recover surfaces of bounded curvature. Chapter-No.7, Chapter-No.8, Chapter-No.12 and Chapter-No.13 are available open access under Creative Commons Attribution-NonCommercial 4.0 International License via link.springer.com.
Book Synopsis Riemannian Manifolds and Homogeneous Geodesics by : Valerii Berestovskii
Download or read book Riemannian Manifolds and Homogeneous Geodesics written by Valerii Berestovskii and published by Springer Nature. This book was released on 2020-11-05 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both classical and modern results, some very recent, many of which are due to the authors. The main focus is on the class of Riemannian manifolds with homogeneous geodesics and on some of its important subclasses. To keep the exposition self-contained the book also includes useful general results not only on geodesic orbit manifolds, but also on smooth and Riemannian manifolds, Lie groups and Lie algebras, homogeneous Riemannian manifolds, and compact homogeneous Riemannian spaces. The intended audience is graduate students and researchers whose work involves differential geometry and transformation groups.
Book Synopsis Modern Geometric Structures and Fields by : Сергей Петрович Новиков
Download or read book Modern Geometric Structures and Fields written by Сергей Петрович Новиков and published by American Mathematical Soc.. This book was released on 2006 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.
Book Synopsis The Geometrical Beauty of Plants by : Johan Gielis
Download or read book The Geometrical Beauty of Plants written by Johan Gielis and published by Springer. This book was released on 2017-06-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the origin of the Gielis curves, surfaces and transformations in the plant sciences. It is shown how these transformations, as a generalization of the Pythagorean Theorem, play an essential role in plant morphology and development. New insights show how plants can be understood as developing mathematical equations, which opens the possibility of directly solving analytically any boundary value problems (stress, diffusion, vibration...) . The book illustrates how form, development and evolution of plants unveil as a musical symphony. The reader will gain insight in how the methods are applicable in many divers scientific and technological fields.
Download or read book Lagerungen written by László Fejes Tóth and published by Springer Nature. This book was released on 2023-04-28 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: The publication of the first edition of Lagerungen in der Ebene, auf der Kugel und im Raum in 1953 marked the birth of discrete geometry. Since then, the book has had a profound and lasting influence on the development of the field. It included many open problems and conjectures, often accompanied by suggestions for their resolution. A good number of new results were surveyed by László Fejes Tóth in his Notes to the 2nd edition. The present version of Lagerungen makes this classic monograph available in English for the first time, with updated Notes, completed by extensive surveys of the state of the art. More precisely, this book consists of: a corrected English translation of the original Lagerungen, the revised and updated Notes on the original text, eight self-contained chapters surveying additional topics in detail. The English edition provides a comprehensive update to an enduring classic. Combining the lucid exposition of the original text with extensive new material, it will be a valuable resource for researchers in discrete geometry for decades to come.
Book Synopsis Noncommutativity and Singularities by : Jean-Pierre Bourguignon
Download or read book Noncommutativity and Singularities written by Jean-Pierre Bourguignon and published by . This book was released on 2009 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two symposia, the Hayashibara Forum and the MSJ/IHÉS joint workshop, were held at the Institute des Hautes Études Scientifiques (IHÉS) in November, 2006. The Hayashibara Forum focused on singularity theory, which has been one of the research areas that has over the years been well represented at IHÉS. The MSJ/IHÉS Joint Workshop, focused on the broad area of noncommutativity, with an emphasis on noncommutative geometry as one of the fundamental themes of 21st century mathematics. This volume contains papers presented at the symposia in the form of invited lectures and contributing talks by young researchers. We believe that the scope of this volume well reflects a new development for singularity theory, and a new direction in mathematics through noncommutativity. This volume are aimed to inspire not only the specialists in these fields but also a wider audience of mathematicians.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America
