论文标题
共构尺寸作为组合模量的关键指数
Conformal Assouad dimension as the critical exponent for combinatorial modulus
论文作者
论文摘要
共构尺寸是公制的准对称变化后所有可能的Assouad尺寸值的最大值。我们表明，对于任何紧凑的双倍度量空间，共构尺寸等于与组合模量相关的关键指数。这概括了Carrasco Piaggio为AHLFORS的常规形式尺寸获得的类似结果，以给更大的空间家族。我们还表明，如果我们在其定义中用幂式对称性替换了甲合管对称性，则不受影响。
The conformal Assouad dimension is the infimum of all possible values of Assouad dimension after a quasisymmetric change of metric. We show that the conformal Assouad dimension equals a critical exponent associated to the combinatorial modulus for any compact doubling metric space. This generalizes a similar result obtained by Carrasco Piaggio for the Ahlfors regular conformal dimension to a larger family of spaces. We also show that the value of conformal Assouad dimension is unaffected if we replace quasisymmetry with power quasisymmetry in its definition.
