论文标题
在某些自符号分形和Weyl的特征值的laplacian：分析方面的调查
The Laplacian on some self-conformal fractals and Weyl's asymptotics for its eigenvalues: A survey of the analytic aspects
论文作者
论文摘要
本文调查了作者最新研究的分析方面，该研究对某些克莱琳群体的“几何规范”的laplacian在圆圈包装上不变（即，在Riemann Sphere上的Möbius转换群体不变（即，Riemann Sphere of Sectractals）的分析方面。 $ \ wideHat {\ mathbb {c}} = \ mathbb {c} \ cup \ {\ infty \} $），包括经典的阿波罗尼亚垫圈和一些圆形的Sierpiński地毯。 Weyl的渐近学特征值的主要结果与Oh和Shah [Invent的形式。数学。 187（2012），1--35，定理1.4]关于圆的渐近分布，在一大批此类分形中。
This article surveys the analytic aspects of the author's recent studies on the construction and analysis of a "geometrically canonical" Laplacian on circle packing fractals invariant with respect to certain Kleinian groups (i.e., discrete groups of Möbius transformations on the Riemann sphere $\widehat{\mathbb{C}}=\mathbb{C}\cup\{\infty\}$), including the classical Apollonian gasket and some round Sierpiński carpets. The main result on Weyl's asymptotics for its eigenvalues is of the same form as that by Oh and Shah [Invent. Math. 187 (2012), 1--35, Theorem 1.4] on the asymptotic distribution of the circles in a very large class of such fractals.
