Conformal surface embeddings and extremal length

Groups, geometry, and dynamics

article

Jeremy Kahn¹  Kevin M. Pilgrim²  Dylan P. Thurston² 

[1] Brown University;Indiana University

关键词: Riemann surfaces with boundary;    conformal embeddings;    extremal length;   

DOI  :  10.4171/ggd/673

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

Given two Riemann surfaces with boundary and a homotopy class of topological embeddings between them, there is a conformal embedding in the homotopy class if and only if the extremal length of every simple closed multi-curve is decreased under the embedding. Furthermore, the homotopy class has a conformal embedding that misses an open disk if and only if extremal lengths are decreased by a definite ratio. This ratio remains bounded away from one under finite covers.

【 授权许可】

CC BY