On the subinvariance of uniform domains in Banach spaces

@article{Huang2012OnTS,
  title={On the subinvariance of uniform domains in Banach spaces},
  author={Manzi Huang and Xiantao Wang and Matti Vuorinen},
  journal={Journal of Mathematical Analysis and Applications},
  year={2012},
  volume={407},
  pages={527-540}
}

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References

SHOWING 1-10 OF 31 REFERENCES
On quasimöbius maps in real Banach spaces
Suppose that E and E′ denote real Banach spaces with dimension at least 2, that D$$ \subseteq $$E and D′ $$ \subseteq $$E′ are domains, that f: D → D′ is an (M,C)-CQH homeomorphism, and that D is
Relatively and inner uniform domains
We generalize the concept of a uniform domain in Banach spaces into two directions. (1) The ordinary metric d of a domain is replaced by a metric e ≥ d, in particular, by the inner metric of the
ON QUASIHYPERBOLIC GEODESICS IN BANACH SPACES
We study properties of quasihyperbolic geodesics on Banach spaces. For example, we show that in a strictly convex Banach space with the Radon-Nikodym property, the quasihy- perbolic geodesics are
Uniform continuity of quasiconformal mappings and conformal deformations
We prove that quasiconformal maps onto domains satisfying a suitable growth condition on the quasihyperbolic metric are uniformly continuous even when both domains are equipped with internal metric.
Dimension-free quasiconformal distortion in $n$-space
Most distortion theorems for K-quasiconformal mappings in Rn, n > 2, depend on both n and K in an essential way, with bounds that become infinite as n tends to oo. The present authors obtain
UNIONS OF JOHN DOMAINS AND UNIFORM DOMAINS IN REAL NORMED VECTOR SPACES
Let E be real normed vector spaces with the dimension at least 2. In this paper we study the following questions: When is the union of two John domains in E a John domain and when is the union of two
Metric space inversions, quasihyperbolic distance, and uniform spaces
We define a notion of inversion valid in the general metric space setting. We establish several basic facts concerning inversions; e.g., they are quasimobius homeomorphisms and quasihyperbolically
CONVEXITY PROPERTIES OF QUASIHYPERBOLIC BALLS ON BANACH SPACES
We study the convexity and starlikeness of metric balls on Banach spaces when the metric is the quasihyperbolic metric or the distance ratio metric. In particular, problems related to these metrics
ISOMETRIES OF SOME HYPERBOLIC-TYPE PATH METRICS, AND THE HYPERBOLIC MEDIAL AXIS PETER HÄSTÖ, ZAIR IBRAGIMOV, DAVID MINDA, SAMINATHAN PONNUSAMY AND SWADESH SAHOO
where |dz| represents integration with respect to path-length, and the infimum is taken over all paths γ joining x, y ∈ D. If p is a C function, then we are in the standard Riemannian setting, but
Quasihyperbolic geodesics in convex domains
We show that quasihyperbolic geodesics exist in convex domains in reflexive Banach spaces and that quasihyperbolic geodesies are quasiconvex in the norm metric in convex domains in all normed spaces.
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