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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An $n$-dimensional space that admits a Poincaré inequality but has no manifold points


Authors: Bruce Hanson and Juha Heinonen
Journal: Proc. Amer. Math. Soc. 128 (2000), 3379-3390
MSC (1991): Primary 43A85; Secondary 28A75
Published electronically: May 18, 2000
MathSciNet review: 1690990
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05453-8
PII: S 0002-9939(00)05453-8
Keywords: Poincaré inequality, Ahlfors $n$-regular, manifold point.
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
Article copyright: © Copyright 2000 American Mathematical Society