The Poincaré Inequality does not improve with blow-up

2015/04/26 by Schioppa, Andrea
#28A80 #31E05 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1504.06858

Abstract

For each β>1 we construct a family F_β of metric measure spaces which is closed under the operation of taking weak-tangents (i.e.~blow-ups), and such that each element of F_β admits a (1,P)-Poincaré inequality if and only if P>β.

Related

• The Poincaré inequality is an open ended condition
• A note on metric-measure spaces supporting Poincaré inequalities
• Sharp Poincaré inequalities under Measure Contraction Property
• Classifying Poincaré Inequalities and the local geometry of RNP-Differentiability Spaces
• Poincaré Inequality Meets Brezis--Van Schaftingen--Yung Formula on Metric Measure Spaces