The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.
On the structure of spaces with Ricci curvature bounded below. I
Open accessAbstract
Fix p and define the renormalized volume function,
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
(1988) · Elsevier eBooks · doi:10.1016/c2013-0-11200-7 · Cited by 5,131
Schwartz, L. (1966) · UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno · Cited by 3,513
Multiple Integrals in the Calculus of Variations
Morrey, C. B. (1966) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-540-69952-1 · Cited by 3,025
Minimal Surfaces and Functions of Bounded Variation
Giusti, E. (1984) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4684-9486-0 · Cited by 2,261
Differential equations on riemannian manifolds and their geometric applications
Cheng, S. Y., & Yau, S. T. (1975) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160280303 · Cited by 930
On the Structure of Complete Manifolds of Nonnegative Curvature
Cheeger, J., & Gromoll, D. (1972) · The Annals of Mathematics · doi:10.2307/1970819 · Cited by 718
Self-citationThe splitting theorem for manifolds of nonnegative Ricci curvature
Cheeger, J., & Gromoll, D. (1971) · Journal of Differential Geometry · doi:10.4310/jdg/1214430220 · Cited by 619
Self-citationLower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products
Cheeger, J., & Colding, T. H. (1996) · The Annals of Mathematics · doi:10.2307/2118589 · Cited by 552
Self-citationStructures métriques pour les variétés riemanniennes
Gromov, M. (1981) · Medical Entomology and Zoology · Cited by 518
A note on the isoperimetric constant
Buser, P. (1982) · Annales scientifiques de l'École normale supérieure · doi:10.24033/asens.1426 · Cited by 479
Cited by
Curvature and injectivity radius estimates for Einstein 4-manifolds
Cheeger, J., & Tian, G. (2005) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-05-00511-4 · Cited by 72
Self-citation
Metadata
- Authors
- Cheeger, J., & Colding, T. H.
- Venue
- Journal of Differential Geometry
- Publisher
- International Press of Boston
- Published
- 1997-01-01
- Volume
- 46
- Issue
- 3
- Pages
- 406-480
- ISSN
- 0022-040X (ISSN-L)
- OpenAlex
- W1870973791
- Cited by
- 817
- References
- 27
- FWCI
- 16.66
- Type
- journal article
- Language
- en
- Open access
- bronze
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: On the structure of spaces with Ricci curvature bounded below. I. https://app.cochat.ai/papers/10.4310/jdg/1214459974
- The paper
- Cheeger, J., & Colding, T. H. (1997). On the structure of spaces with Ricci curvature bounded below. I. Journal of Differential Geometry. https://doi.org/10.4310/jdg/1214459974
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
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.
