An Invitation to Alexandrov Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Invitation to Alexandrov Geometry write by Stephanie Alexander. This book was released on 2019-05-08. An Invitation to Alexandrov Geometry available in PDF, EPUB and Kindle. Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.
Alexandrov Geometry
Alexandrov Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Alexandrov Geometry write by Stephanie Alexander. This book was released on 2024-05-23. Alexandrov Geometry available in PDF, EPUB and Kindle. Alexandrov spaces are defined via axioms similar to those of the Euclid axioms but where certain equalities are replaced with inequalities. Depending on the signs of the inequalities, we obtain Alexandrov spaces with curvature bounded above (CBA) and curvature bounded below (CBB). Even though the definitions of the two classes of spaces are similar, their properties and known applications are quite different. The goal of this book is to give a comprehensive exposition of the structure theory of Alexandrov spaces with curvature bounded above and below. It includes all the basic material as well as selected topics inspired by considering Alexandrov spaces with CBA and with CBB simultaneously. The book also includes an extensive problem list with solutions indicated for every problem.
Recent Advances in Alexandrov Geometry
Recent Advances in Alexandrov Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Recent Advances in Alexandrov Geometry write by Gerardo Arizmendi Echegaray. This book was released on 2022-10-27. Recent Advances in Alexandrov Geometry available in PDF, EPUB and Kindle. 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.
Pure Metric Geometry
Pure Metric Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Pure Metric Geometry write by Anton Petrunin. This book was released on 2023-12-23. Pure Metric Geometry available in PDF, EPUB and Kindle. This book serves as an introductory asset for learning metric geometry by delivering an in-depth examination of key constructions and providing an analysis of universal spaces, injective spaces, the Gromov-Hausdorff convergence, and ultralimits. This book illustrates basic examples of domestic affairs of metric spaces, this includes Alexandrov geometry, geometric group theory, metric-measure spaces and optimal transport. Researchers in metric geometry will find this book appealing and helpful, in addition to graduate students in mathematics, and advanced undergraduate students in need of an introduction to metric geometry. Any previous knowledge of classical geometry, differential geometry, topology, and real analysis will be useful in understanding the presented topics.
A.D. Alexandrov
A.D. Alexandrov - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A.D. Alexandrov write by S.S. Kutateladze. This book was released on 2005-07-25. A.D. Alexandrov available in PDF, EPUB and Kindle. 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
