论文标题
AHLFORS常规的保形维度和Gromov-Hausdorff收敛
Ahlfors regular conformal dimension and Gromov-Hausdorff convergence
论文作者
论文摘要
我们证明，与Gromov-Hausdorff收敛相对于Gromov-Hausdorff收敛时，AHLFORS的常规保形尺寸仅限于统一完美的，均匀的准中性度量空间时。此外，如果在$Δ$δ$δ$δ$ hymyperbolic度量空间的均匀限制的codiameter组的离散，Quasiconvex-Cocompact组的极限集的情况下，我们显示了AHLFOR的常规保串尺寸的连续性。
We prove that the Ahlfors regular conformal dimension is upper semicontinuous with respect to Gromov-Hausdorff convergence when restricted to the class of uniformly perfect, uniformly quasi-selfsimilar metric spaces. Moreover we show the continuity of the Ahlfors regular conformal dimension in case of limit sets of discrete, quasiconvex-cocompact group of isometries of uniformly bounded codiameter of $δ$-hyperbolic metric spaces under equivariant pointed Gromov-Hausdorff convergence of the spaces.
