Green's functions, harmonic functions, and volume comparison
Open accessThe 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
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.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
SOB(β) Riemannian manifolds are nonparabolic if and only if β > 2.
“From Li-Tam [39], SOB(β) Riemannian manifolds are nonparabolic if and only if β > 2.”
From Gravitational instantons from rational elliptic surfaces (2011) · cites this paper as [39]
The Introduction and §1 relate nonparabolicity to the existence of a positive Green’s function and give a volume-growth integral criterion under curvature and volume-comparison assumptions. The paper does not define SOB(β) or state the claimed β > 2 equivalence for that class, so the cited result supports the underlying criterion but not its stated scope. (LLM, conf=0.78)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
No references could be resolved yet.
Research works printed but not linked: 7
- R. Bishop & R. Crittenden, Geometry of manifolds, Academic Press, New York, 1964.
- M. Cai, T. H. Colding, & D. Yang, A gap theorem for ends of complete manifolds, preprint.
- S. Y. Cheng, Finite dimensionality of the spaces of positive and bounded harmonic func- tions, preprint.
- Harmonic functions with growth conditions on a manifold of asymptotically non- negative curvature I, Geometry and Analysis on Manifolds, Lecture Notes in Math., Vol. 1339, Springer, Berlin, 1988, 158-181.
- Z-D. Liu, Ball covering on manifolds with nonnegative Ricci curvature near infinity, preprint.
- C.-J. Sung, Harmonic functions under quasi-isometry, preprint.
- Potential theory and diffusion on Riemannian manifolds, Conf. on Harmonic Analysis in Honor of Antoni Zygmund, Vols. I, II, Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, 821-837.
Cited by
Sorted by citations
Gravitational instantons from rational elliptic surfaces
Hein, H.-J. (2011) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-2011-00723-6 · Cited by 87 · see citing works
- Authors
- Li, P., & Tam, L.-F.
- Venue
- Journal of Differential Geometry
- Publisher
- International Press of Boston
- Published
- 1995-01-01
- Volume
- 41
- Issue
- 2
- Pages
- 277-318
- ISSN
- 0022-040X (ISSN-L)
- OpenAlex
- W1500414901
- Cited by
- 85
- References
- 0
- Citations by year
- 2026: 2 · 2025: 1 · 2024: 2 · 2023: 1 · 2022: 1 · 2021: 6 · 2020: 3 · 2019: 3 · 2018: 2 · 2017: 1 · 2016: 1 · 2015: 5 · 2013: 3 · 2012: 2
- FWCI
- 9.71
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Differential Geometry (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Funders
- National Science Foundation (9300422)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- Green's function, harmonic functions, volume comparison, Riemannian manifolds, Ricci curvature
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
