English

The Poincar\'e Inequality does not improve with blow-up

Metric Geometry 2016-01-14 v2 Differential Geometry

Abstract

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

Keywords

Cite

@article{arxiv.1504.06858,
  title  = {The Poincar\'e Inequality does not improve with blow-up},
  author = {Andrea Schioppa},
  journal= {arXiv preprint arXiv:1504.06858},
  year   = {2016}
}

Comments

Added friendlier description of Graph; changed font to 12pt

R2 v1 2026-06-22T09:22:54.260Z