Results 1 
3 of
3
HYPERBOLIC AND UNIFORM DOMAINS IN BANACH SPACES
"... Abstract. A domain G in a Banach space is said to be δhyperbolic if it is a Gromov δhyperbolic space in the quasihyperbolic metric. Then G has the Gromov boundary ∂ ∗ G and the norm boundary ∂G. We show that the following properties are quantitatively equivalent: (1) G is Cuniform. (2) G is δhy ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
Abstract. A domain G in a Banach space is said to be δhyperbolic if it is a Gromov δhyperbolic space in the quasihyperbolic metric. Then G has the Gromov boundary ∂ ∗ G and the norm boundary ∂G. We show that the following properties are quantitatively equivalent: (1) G is Cuniform. (2) G is δhyperbolic and there is a natural bijective map G ∪ ∂ ∗ G → G ∪ ∂G, which is ηquasimöbius rel ∂ ∗ G. (3) G is δhyperbolic and there is a natural ηquasimöbius homeomorphism ∂ ∗ G → ∂G. In a euclidean space, this improves a result of BonkHeinonenKoskela, whose estimates depend on dimension and on a base point. MSC Subject Classification: 30C65, 53C23. 1
ON JOHN DOMAINS IN BANACH SPACES
"... Abstract. We study the stability of John domains in Banach spaces under removal of a countable set of points. In particular, we prove that the class of John domains is stable in the sense that removing a certain type of closed countable set from the domain yields a new domain which also is a John d ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We study the stability of John domains in Banach spaces under removal of a countable set of points. In particular, we prove that the class of John domains is stable in the sense that removing a certain type of closed countable set from the domain yields a new domain which also is a John domain. We apply this result to prove the stability of the inner uniform domains. Finally, we consider a wider class of domains, so called ψJohn domains and prove a similar result for this class. 1.