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Nonpositive Curvature: Geometric and Analytic Aspects (Lectures in Mathematics. ETH Zürich)

Jürgen Jost

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Description: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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Nonpositive Curvature: Geometric and Analytic Aspects (Lectures in Mathematics. ETH Zürich). To get started finding Nonpositive Curvature: Geometric and Analytic Aspects (Lectures in Mathematics. ETH Zürich), you are right to find our website which has a comprehensive collection of manuals listed.
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ISBN: 3764357363

Description: 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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Nonpositive Curvature: Geometric and Analytic Aspects (Lectures in Mathematics. ETH Zürich). To get started finding Nonpositive Curvature: Geometric and Analytic Aspects (Lectures in Mathematics. ETH Zürich), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Nonpositive Curvature: Geometric and Analytic Aspects (Lectures in Mathematics. ETH Zürich)

Nonpositive Curvature: Geometric and Analytic Aspects (Lectures in Mathematics. ETH Zürich)

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