An $n$-dimensional space that admits a Poincaré inequality but has no manifold points
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- by Bruce Hanson and Juha Heinonen PDF
- Proc. Amer. Math. Soc. 128 (2000), 3379-3390 Request permission
Abstract:
For each integer $n\ge 2$ we construct a compact, geodesic metric space $X$ which has topological dimension $n$, is Ahlfors $n$-regular, satisfies the Poincaré inequality, possesses $\mathbb R^n$ as a unique tangent cone at $\mathcal {H}_n$ almost every point, but has no manifold points.References
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Additional Information
- Bruce Hanson
- Affiliation: Department of Mathematics, St. Olaf College, Northfield, Minnesota 55057
- Email: hansonb@stolaf.edu
- Juha Heinonen
- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
- Received by editor(s): August 14, 1998
- Received by editor(s) in revised form: January 18, 1999
- Published electronically: May 18, 2000
- Additional Notes: The second author was supported by NSF grant DMS 96-22844
- Communicated by: Albert Baernstein II
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3379-3390
- MSC (1991): Primary 43A85; Secondary 28A75
- DOI: https://doi.org/10.1090/S0002-9939-00-05453-8
- MathSciNet review: 1690990