Displaying similar documents to “The Carathéodory topology for multiply connected domains I”

The Carathéodory topology for multiply connected domains II

Mark Comerford (2014)

Open Mathematics

Similarity:

We continue our exposition concerning the Carathéodory topology for multiply connected domains which we began in [Comerford M., The Carathéodory topology for multiply connected domains I, Cent. Eur. J. Math., 2013, 11(2), 322–340] by introducing the notion of boundedness for a family of pointed domains of the same connectivity. The limit of a convergent sequence of n-connected domains which is bounded in this sense is again n-connected and will satisfy the same bounds. We prove a result...

Generalized John disks

Chang-Yu Guo, Pekka Koskela (2014)

Open Mathematics

Similarity:

We establish the basic properties of the class of generalized simply connected John domains.

Short separating geodesics for multiply connected domains

Mark Comerford (2011)

Open Mathematics

Similarity:

We consider the following questions: given a hyperbolic plane domain and a separation of its complement into two disjoint closed sets each of which contains at least two points, what is the shortest closed hyperbolic geodesic which separates these sets and is it a simple closed curve? We show that a shortest geodesic always exists although in general it may not be simple. However, one can also always find a shortest simple curve and we call such a geodesic a meridian of the domain. We...