Riemannian center of mass and mollifier smoothing
Integrity signals
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There are results on the non-emptiness and the uniqueness of Fréchet means for manifolds.
“There are results on the non-emptiness and the uniqueness of Fr´ echet means for manifolds (Karcher 1977, Kendall 1990).”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Karcher 1977
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Multiclass Brain–Computer Interface Classification by Riemannian Geometry
Barachant, A., Bonnet, S., Congedo, M., & Jutten, C. (2012) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2011.2172210 · Cited by 878 · see citing works
Probability measures on the space of persistence diagrams
Mileyko, Y., Mukherjee, S., & Harer, J. (2011) · Inverse Problems · doi:10.1088/0266-5611/27/12/124007 · Cited by 249 · see citing works
Topological pattern recognition for point cloud data
Carlsson, G. (2014) · Acta Numerica · doi:10.1017/s0962492914000051 · Cited by 230 · see citing works
Hayat, M., Bennamoun, M., & El-Sallam, A. A. (2013) · 2013 IEEE Workshop on Applications of Computer Vision (WACV) · doi:10.1109/wacv.2013.6475003 · Cited by 14 · see citing works
- Authors
- Karcher, H.
- Affiliations
- University of Bonn (DE)
- Corresponding author
- Karcher, H.
- Venue
- Communications on Pure and Applied Mathematics
- Publisher
- Wiley
- Published
- 1977-09
- Volume
- 30
- Issue
- 5
- Pages
- 509-541
- ISSN
- 0010-3640 (ISSN-L)
- 1097-0312
- OpenAlex
- W2109409043
- Cited by
- 995
- References
- 0
- Citations by year
- 2026: 18 · 2025: 27 · 2024: 42 · 2023: 38 · 2022: 39 · 2021: 48 · 2020: 66 · 2019: 47 · 2018: 48 · 2017: 50 · 2016: 63 · 2015: 53 · 2014: 54 · 2013: 55 · 2012: 62
- FWCI
- 2.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Communications on Pure and Applied Mathematics (publishedVersion)
- 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 › Applied Mathematics › Mathematical Inequalities and Applications
- Keywords
- Riemannian geometry, optimal transport, gradient flow, mean curvature flow, Riemannian manifolds
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.
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