Q-正则Loewner空间中的拟对称映射

Quasisymmetric Maps in Q-Regular Loewner Spaces

本文在Q-正则Loewner空间中用环模不等式刻划了拟对称映射.另外,在 Q-维Ahlfors-David正则空间中建立了拟对称映射作用下的Grotzsch-Teichmuller型 模不等式,它是通过伸张系数的积分平均来表示.

In this paper, we characterize the quasisymmetric maps by modulus inequalities of rings in Q-regular Loewner spaces. Furthermore, we establish the Grotzsch-Teichmuller type modulus inequality for quasisymmetric maps between Q-dimensional Ahlfors-David regular spaces, which is expressed in terms of the integral mean value of dilatation coefficients.