The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
Hyperbolic Groups
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In the citing paper
“Following prior work, we first advocate for using hyperbolic spaces which provably model tree-like structures better than Euclidean geometry.”
From Hyperbolic Entailment Cones for Learning Hierarchical Embeddings (2018) · cites this paper as Gromov, 1987
In the citing paper
“For instance, the Euclidean space R n for n ≥ 2 is not δ -hyperbolic for any δ ≥ 0 , while the Poincar´ e ball D n is log(1+ √ 2) -hyperbolic.”
From Hyperbolic Entailment Cones for Learning Hierarchical Embeddings (2018) · cites this paper as Gromov, 1987
In the citing paper
“Theorem : For any δ > 0 , any δ -hyperbolic metric space ( X,d X ) and any set of points x 1 , ..., x n ∈ X , there exists a finite weighted tree ( T, d T ) and an embedding f : T → X such that for all i, j ,”
From Hyperbolic Entailment Cones for Learning Hierarchical Embeddings (2018) · cites this paper as Gromov, 1987
In the citing paper
“This exponential growth property enables hyperbolic spaces to embed any weighted tree while almost preserving their metric 3 (Gromov, 1987; Bowditch, 2006; Sarkar, 2011).”
From Hyperbolic Entailment Cones for Learning Hierarchical Embeddings (2018) · cites this paper as Gromov, 1987
Citations
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Metadata
- Authors
- Gromov, M.
- Corresponding author
- Gromov, M.
- Venue
- Mathematical Sciences Research Institute Publications
- Publisher
- Springer New York
- Published
- 1987
- Pages
- 75-263
- ISSN
- 0940-4740 (ISSN-L)
- OpenAlex
- W4235484205
- Cited by
- 1,817
- References
- 19
- Citations by year
- 2026: 41 · 2025: 106 · 2024: 94 · 2023: 92 · 2022: 87 · 2021: 90 · 2020: 72 · 2019: 69 · 2018: 72 · 2017: 82 · 2016: 79 · 2015: 75 · 2014: 68 · 2013: 66 · 2012: 54
- FWCI
- 19.75
- Type
- book chapter
- Language
- en
- Open access
- closed
- Locations
- Mathematical Sciences Research Institute publications (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Physical Sciences › Mathematics › Geometry and Topology › Mathematics and Applications
- Keywords
- hyperbolic groups, Gromov hyperbolicity, geometric group theory, Cayley graphs, word metric, hyperbolic geometry
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