The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Diameter-extremal subsets of spheres
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“Such a bound was originally conjectured in[5].”
From An inequality for anti-self-polar polytopes (2026) · cites this paper as [5]
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Cites
Comparison Theorems in Riemannian Geometry
Cheeger, J., & Ebin, D. (2008) · American Mathematical Society eBooks · doi:10.1090/chel/365 · Cited by 970
Gromov, M. (1983) · Journal of Differential Geometry · doi:10.4310/jdg/1214509283 · Cited by 867
Lagerungen in der Ebene auf der Kugel und im Raum
Tóth, L. F. (1972) · Springer eBooks · doi:10.1007/978-3-642-65234-9 · Cited by 578
Comparison Theorems in Riemannian Geometry
Eschenburg, J.-H. (1975) · North-Holland mathematical library · doi:10.1016/s0924-6509(08)x7013-8 · Cited by 546
Drei Sätze über die n-dimensionale euklidische Sphäre
Borsuk, K. (1933) · Fundamenta Mathematicae · doi:10.4064/fm-20-1-177-190 · Cited by 516
The number of faces of a simplicial convex polytope
Stanley, R. P. (1980) · Advances in Mathematics · doi:10.1016/0001-8708(80)90050-x · Cited by 451
Curvature, diameter and betti numbers
Gromov, M. (1981) · Commentarii Mathematici Helvetici · doi:10.1007/bf02566208 · Cited by 353
Convex polytopes and the upper bound conjecture
McMullen, P., Shephard, G. C., Reeve, J. E., et al. (1971) · Cambridge University Press eBooks · Cited by 337
Grove, K., & Shiohama, K. (1977) · The Annals of Mathematics · doi:10.2307/1971164 · Cited by 286
A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes
Billera, L. J., & Lee, C. W. (1981) · Journal of Combinatorial Theory Series A · doi:10.1016/0097-3165(81)90058-3 · Cited by 211
The numbers of faces of simplicial polytopes
McMullen, P. (1971) · Israel Journal of Mathematics · doi:10.1007/bf02771471 · Cited by 208
The lower bound conjecture for 3- and 4-manifolds
Walkup, D. W. (1970) · Acta Mathematica · doi:10.1007/bf02392331 · Cited by 145
Beweis einer Vermutung von A. Vázsonyi
Heppes, A. (1956) · Acta Mathematica Academiae Scientiarum Hungaricae · doi:10.1007/bf02020540 · Cited by 66
The filling radius of two-point homogeneous spaces
Katz, M. G. (1983) · Journal of Differential Geometry · doi:10.4310/jdg/1214437785 · Cited by 56
Self-citationÜber eine Übertragung des Hellyschen Satzes in Sphärische Räume
Molnár, J. (1957) · Acta Mathematica Academiae Scientiarum Hungaricae · doi:10.1007/bf02020320 · Cited by 15
Research works printed but not linked: 3
- B. Grünbaum, A proof of Vázsonyi's conjecture,Bull. Res. Council Israel A 6 (1956), 77–78.
- L. Lovász, Self-dual polytopes and the chromatic number of distance graphs on the sphere,Acta Sci. Math. 45 (1983), 317–323.
- S. Straszewicz, Sur un problème géométrique de P. Erdös,Bull. Acad. Polon. Sci. Cl. III 5 (1957), 39–40.
Cited by
An inequality for anti-self-polar polytopes
Katz, M. G. (2026) · The Mathematical Intelligencer · doi:10.1007/s00283-025-10452-8
“The article Katz (1989) investigated 4 -dimensional anti- self-polar polytopes as a possible source of counterexamples to Borsuk’s conjecture in ℝ 4 (no counterexamples in this dimension have been found as yet, however).”
InfluentialSelf-citation
Metadata
- Authors
- Katz, M.
- Affiliations
- State University of New York (US)
- Corresponding author
- Katz, Mikhail
- ORCID
- Katz, Mikhail
- Venue
- Discrete & Computational Geometry
- Published
- 1989-03
- Volume
- 4
- Issue
- 2
- Pages
- 117-137
- ISSN
- 0179-5376 (ISSN-L)
- 1432-0444
- OpenAlex
- W1991627407
- Cited by
- 12
- References
- 15
- Citations by year
- 2025: 3 · 2024: 2 · 2022: 2 · 2021: 1 · 2019: 1
- FWCI
- 1.40
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Discrete & Computational Geometry (publishedVersion)
- Funders
- National Science Foundation (8602645)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Point processes and geometric inequalities
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computational Geometry and Mesh Generation
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Keywords
- Hausdorff distance
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
