Equivalence of the Apollonian and Its Inner Metric

In this paper we show that the equivalence of the Apollonian metric and its inner metric remains unchanged by the removal of a point from the domain. For this we need to assume that the complement of the domain is not contained in a hyperplane. This improves a result of the authors wherein the same conclusion was reached under the stronger assumption that the domain contains an exterior point.

• Type: Journal
• Year: 2010
• Where: IJMMSC
• Authors: Peter Hästö, S. Ponnusamy, Swadesh K. Sahoo
• Keywords: Exterior Point, IJMMSC 2010, Metric, Stronger Assumption