Inner Uniform Domains, the Quasihyperbolic Metric and Weak Bloch Functions

Abstract

Abstract. We characterize the class of inner uniform domains in terms of the quasihyperbolic metric and the quasihyperbolic geodesic. We also characterize uniform domains and inner uniform domains in terms of weak Bloch functions.

The Quasisymmetric Mappings under the Quasihyperbolic Metric in Real Banach Spaces

“…Te QH metric of a domain in R n was introduced by Gehring and Palka [16]. Tis metric was later generalized to the setting of Banach spaces and metric spaces and has become an important tool in the study of geometric function theory [9,10,13,[17][18][19][20].…”

Inner Uniform Domains and the Apollonian Inner Metric

“…Moreover, in [13], the authors proved the following. See [3,4,6,13,15,16,17,21,22,24] for more details on uniform domains and inner uniform domains.…”