The Grushin hemisphere as a Ricci limit space with curvature $\ge 1$
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- by Jiayin Pan
- Proc. Amer. Math. Soc. Ser. B 10 (2023), 71-75
- DOI: https://doi.org/10.1090/bproc/160
- Published electronically: March 24, 2023
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Abstract:
The Grushin sphere is an almost-Riemannian manifold that degenerates along its equator. We construct a sequence of Riemannian metrics on a sphere $S^{m+n}$ with $Ric\ge 1$ such that its Gromov-Hausdorff limit is the $n$-dimensional Grushin hemisphere.References
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Bibliographic Information
- Jiayin Pan
- Affiliation: Department of Mathematics, University of California, Santa Cruz, California
- MR Author ID: 1356847
- ORCID: 0000-0002-4892-4793
- Email: jpan53@ucsc.edu
- Received by editor(s): January 17, 2023
- Published electronically: March 24, 2023
- Communicated by: Lu Wang
- © Copyright 2023 by the author under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License (CC BY NC ND 4.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 10 (2023), 71-75
- MSC (2020): Primary 53C23, 53C20
- DOI: https://doi.org/10.1090/bproc/160
- MathSciNet review: 4566173