Geodesic
The Poincaré inequality is an open ended condition
Stephen Keith1 ; Xiao Zhong2
1Mathematical Sciences Institute<br/>Australian National University<br/>Canberra 0200<br/>Australia
2Department of Mathematics and Statistics<br/>University of Jyväskylä<br/>Jyväskylä<br/>Finland
Annals of mathematics, Tome 167 (2008) no. 2, pp. 575-599
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Let $p >1$ and let $(X,d,\mu)$ be a complete metric measure space with $\mu$ Borel and doubling that admits a $(1,p)$-Poincaré inequality. Then there exists $\varepsilon >0$ such that $(X,d,\mu)$ admits a $(1,q)$-Poincaré inequality for every $q >p – \varepsilon$, quantitatively.

DOI : 10.4007/annals.2008.167.575

Stephen Keith  1   ; Xiao Zhong  2

1 Mathematical Sciences Institute<br/>Australian National University<br/>Canberra 0200<br/>Australia
2 Department of Mathematics and Statistics<br/>University of Jyväskylä<br/>Jyväskylä<br/>Finland 
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     title = {The {Poincar\'e} inequality is an open ended condition},
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Stephen Keith; Xiao Zhong. The Poincaré inequality is an open ended condition. Annals of mathematics, Tome 167 (2008) no. 2, pp. 575-599. doi: 10.4007/annals.2008.167.575

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