This book discusses various geometric and analytic aspects of nonpositive curvature, starting with a discussion of Riemannian examples and rigidity theorems. It then treats generalized notions of nonpositive curvature in metric geometry in the sense of Alexandrov and Busemann, as well as the theory of harmonic maps with values in such spaces. It is intended for researchers and graduate students in Riemannian and metric geometry as well as calculus of variations.
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"Recollects some basic properties as well as some fairly advanced results [which] is done with a spirit that allows one to understand that, even though the study of such manifolds has important differences from the flat case, some techniques come from the very elementary Euclidean geometry." --Mathematical Reviews
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First Sentence:
Examples of Riemannian manifolds of negative or nonpositive sectional curvature Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
geodesic length space, generalized harmonic maps, nonpositive sectional curvature, nonpositive curvature, noncompact type, shortest geodesic, hyperbolic groups, rigidity theorem, trivial center, isometry group, symmetric spaces, negative curvature, moduli space, minimizing sequence Key Phrases - Capitalized Phrases (CAPs): (learn more)
Euclidean Bruhat-Tits, The Bochner New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Examples of Riemannian manifolds of negative or nonpositive sectional curvature Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
geodesic length space, generalized harmonic maps, nonpositive sectional curvature, nonpositive curvature, noncompact type, shortest geodesic, hyperbolic groups, rigidity theorem, trivial center, isometry group, symmetric spaces, negative curvature, moduli space, minimizing sequence Key Phrases - Capitalized Phrases (CAPs): (learn more)
Euclidean Bruhat-Tits, The Bochner New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 5
books:
3
books
cite this book:
- Differentiable Manifolds by Lawrence Conlon in Back Matter
- Differential Geometry (Proceedings of Symposia in Pure Mathematics, vol. 27, pt. 2) by Shiing-Shen Chern in Back Matter
- Calculus of Variations (Cambridge Studies in Advanced Mathematics) by Jürgen Jost in Back Matter
- Differential Geometry (Proceedings of Symposia in Pure Mathematics ; V. 54 Part 1, 2, 3) (Pt.1-3) by Robert Greene in Back Matter
- Geometry of Foliations (Monographs in Mathematics) by Philippe Tondeur in Back Matter
- Partial Differential Equations by Jürgen Jost on page 317
- Riemannian Geometry: A Modern Introduction (Cambridge Studies in Advanced Mathematics) by Isaac Chavel in Back Matter
- Calculus of Variations (Cambridge Studies in Advanced Mathematics) by Jürgen Jost on page 195
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