Nonpositive Curvature: Geometric and Analytic Aspects - 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 Nonpositive Curvature: Geometric and Analytic Aspects write by Jürgen Jost. This book was released on 1997-05-01. Nonpositive Curvature: Geometric and Analytic Aspects available in PDF, EPUB and Kindle. The present book contains the lecture notes from a "Nachdiplomvorlesung", a topics course adressed to Ph. D. students, at the ETH ZUrich during the winter term 95/96. Consequently, these notes are arranged according to the requirements of organizing the material for oral exposition, and the level of difficulty and the exposition were adjusted to the audience in Zurich. The aim of the course was to introduce some geometric and analytic concepts that have been found useful in advancing our understanding of spaces of nonpos itive curvature. In particular in recent years, it has been realized that often it is useful for a systematic understanding not to restrict the attention to Riemannian manifolds only, but to consider more general classes of metric spaces of generalized nonpositive curvature. The basic idea is to isolate a property that on one hand can be formulated solely in terms of the distance function and on the other hand is characteristic of nonpositive sectional curvature on a Riemannian manifold, and then to take this property as an axiom for defining a metric space of nonposi tive curvature. Such constructions have been put forward by Wald, Alexandrov, Busemann, and others, and they will be systematically explored in Chapter 2. Our focus and treatment will often be different from the existing literature. In the first Chapter, we consider several classes of examples of Riemannian manifolds of nonpositive curvature, and we explain how conditions about nonpos itivity or negativity of curvature can be exploited in various geometric contexts.
Nonpositive Curvature: Geometric and Analytic Aspects
Nonpositive Curvature: Geometric and Analytic Aspects - 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 Nonpositive Curvature: Geometric and Analytic Aspects write by Jürgen Jost. This book was released on 2012-12-06. Nonpositive Curvature: Geometric and Analytic Aspects available in PDF, EPUB and Kindle. The present book contains the lecture notes from a "Nachdiplomvorlesung", a topics course adressed to Ph. D. students, at the ETH ZUrich during the winter term 95/96. Consequently, these notes are arranged according to the requirements of organizing the material for oral exposition, and the level of difficulty and the exposition were adjusted to the audience in Zurich. The aim of the course was to introduce some geometric and analytic concepts that have been found useful in advancing our understanding of spaces of nonpos itive curvature. In particular in recent years, it has been realized that often it is useful for a systematic understanding not to restrict the attention to Riemannian manifolds only, but to consider more general classes of metric spaces of generalized nonpositive curvature. The basic idea is to isolate a property that on one hand can be formulated solely in terms of the distance function and on the other hand is characteristic of nonpositive sectional curvature on a Riemannian manifold, and then to take this property as an axiom for defining a metric space of nonposi tive curvature. Such constructions have been put forward by Wald, Alexandrov, Busemann, and others, and they will be systematically explored in Chapter 2. Our focus and treatment will often be different from the existing literature. In the first Chapter, we consider several classes of examples of Riemannian manifolds of nonpositive curvature, and we explain how conditions about nonpos itivity or negativity of curvature can be exploited in various geometric contexts.
Riemannian Geometry and Geometric Analysis
Riemannian Geometry and 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 Riemannian Geometry and Geometric Analysis write by Jürgen Jost. This book was released on 2013-11-11. Riemannian Geometry and Geometric Analysis available in PDF, EPUB and Kindle. FROM REVIEWS OF THE FIRST EDITION "a very readable introduction to Riemannian geometry...it is most welcome...The book is made more interesting by the perspectives in various sections, where the author mentions the history and development of the material and provides the reader with references."-MATHEMATICAL REVIEWS
Geometric Analysis and Nonlinear Partial Differential Equations
Geometric Analysis and Nonlinear Partial Differential Equations - 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 Geometric Analysis and Nonlinear Partial Differential Equations write by Stefan Hildebrandt. This book was released on 2012-12-06. Geometric Analysis and Nonlinear Partial Differential Equations available in PDF, EPUB and Kindle. This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.
Metric Spaces, Convexity and Nonpositive Curvature
Metric Spaces, Convexity and Nonpositive Curvature - 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 Metric Spaces, Convexity and Nonpositive Curvature write by Athanase Papadopoulos. This book was released on 2005. Metric Spaces, Convexity and Nonpositive Curvature available in PDF, EPUB and Kindle.
