How Long to Read Lectures on Spaces of Nonpositive Curvature

How Long Does it Take to Read Lectures on Spaces of Nonpositive Curvature?

It takes the average reader 1 hour and 55 minutes to read Lectures on Spaces of Nonpositive Curvature by Werner Ballmann

Assuming a reading speed of 250 words per minute. Learn more

Description

Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory.

How long is Lectures on Spaces of Nonpositive Curvature?

Lectures on Spaces of Nonpositive Curvature by Werner Ballmann is 114 pages long, and a total of 28,956 words.

This makes it 38% the length of the average book. It also has 35% more words than the average book.

How Long Does it Take to Read Lectures on Spaces of Nonpositive Curvature Aloud?

The average oral reading speed is 183 words per minute. This means it takes 2 hours and 38 minutes to read Lectures on Spaces of Nonpositive Curvature aloud.

What Reading Level is Lectures on Spaces of Nonpositive Curvature?

Lectures on Spaces of Nonpositive Curvature is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Lectures on Spaces of Nonpositive Curvature?

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