Local convexity properties of Apollonian and Seittenranta's metric balls
  We consider local convexity properties of balls in the Apollonian and Seittenranta's metrics. Balls in the Apollonian metric are considered in the twice punctured space and starlike domains. Balls in Seittenranta's metric are considered in the twice punctured space and in the punctured ball. 
Riku Kl\'en
math.MG