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.
An Invitation to Alexandrov Geometry
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.
Recent Advances in Geometric Analysis
Recent Advances in Geometric Analysis - 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 Geometric Analysis write by Yng-Ing Lee. This book was released on 2010. Recent Advances in Geometric Analysis available in PDF, EPUB and Kindle. Explores recent advances in geometric analysis and related topics, including Ricci flow, affine normal flow, geometric analysis on pseudo-convex hypersurfaces, Alexandrov space, manifolds with special holonomy, and the singular plateau problem. It is intended for both researchers and graduate students studying geometric analysis and related areas.
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 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.
A. D. Alexandrov Selected Works
A. D. Alexandrov Selected Works - 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 Selected Works write by Yu. G. Reshetnyak. This book was released on 2002-02-21. A. D. Alexandrov Selected Works available in PDF, EPUB and Kindle. 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.
