The Poincaré Inequality Does Not Improve with Blow-Up
Andrea Schioppa
Analysis and Geometry in Metric Spaces, Tome 4 (2016), / Harvested from 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.

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:288016 
@article{bwmeta1.element.doi-10_1515_agms-2016-0018,
     author = {Andrea Schioppa},
     title = {The Poincar\'e Inequality Does Not Improve with Blow-Up},
     journal = {Analysis and Geometry in Metric Spaces},
     volume = {4},
     year = {2016},
     zbl = {06676755},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2016-0018}
}

Andrea Schioppa. The Poincaré Inequality Does Not Improve with Blow-Up. Analysis and Geometry in Metric Spaces, Tome 4 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2016-0018/