Geodesic
The Poincaré Inequality Does Not Improve with Blow-Up
Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

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For each β > 1 we construct a family Fβ of metric measure spaces which is closed under the operation of taking weak-tangents (i.e. blow-ups), and such that each element of Fβ admits a (1, P)-Poincaré inequality if and only if P > β.
Mots-clés : Poincaré inequality, modulus 
@article{AGMS_2016_4_1_a18,
     author = {Schioppa, Andrea},
     title = {The {Poincar\'e} {Inequality} {Does} {Not} {Improve} with {Blow-Up}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2016},
     volume = {4},
     number = {1},
     zbl = {06676755},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2016_4_1_a18/}
}
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Schioppa, Andrea. The Poincaré Inequality Does Not Improve with Blow-Up. Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2016_4_1_a18/