Metric Spaces of Non-Positive Curvature

Bridson, M. R., & Haefliger, A. (1999). Metric Spaces of Non-Positive Curvature. Springer.

Type

Book

Intellectual base

Review or monograph

Year

1999

Volume

4

Issue

1

DOI

10.1007/978-3-662-12494-9

ISBN

9783642083990

DOI registrant

Springer Nature

Link

https://egg.epfl.ch/metriques/Bridson-Haefliger.pdf

Cited by

5 citations across 5 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Gromov's compactness theorem (geometry)
  • Gromov's metric compactness theorem gives conditions ensuring every sequence in a family has a Gromov–Hausdorff convergent subsequence.
• Hadamard manifold
  • … the Riemannian metric is complete, simple connectivity holds, sectional curvature is nonpositive everywhere, and the invoked geodesic and exponential-map consequences have their hypotheses. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..
• Hadamard space
  • Hadamard spaces generalize Hilbert spaces and simply connected complete nonpositively curved manifolds, giving unique geodesics, convex distance and well-defined metric projections and barycenters.
• Midpoint
  • These are related realizations of segment halving, not permission to average arbitrary points without an affine structure.

    This sourceNumeric tree placement and intrinsic-circle two-arc counterexample are editorial deductions.

• Word metric
  • After choosing a symmetric generating set S, distance from g to h is the minimum S-word length of g inverse h; finite generating sets yield metrics equivalent up to quasi-isometry.

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