Abstract 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.

中文翻译：

---

庞加莱不等式不会随着爆炸而改善

摘要 对于每个 β > 1，我们构造了一个度量测度空间族 Fβ，它在取弱切线（即爆炸）的操作下是封闭的，并且使得 Fβ 的每个元素都承认 (1, P)-Poincaré 不等式当且仅当 P > β。