In a small pan over medium-high heat, bring apple juice, pomegranate juice, orange rind, and cinnamon stick to a boil.
Place pears face down in the pan. Lower heat and simmer gently until a knife inserted into the pears meets no resistance, about 10-20 minutes, spooning the sauce over the pears as they cook. Once the pears are tender, remove from heat and let cool.
Over medium-low heat, reduce the remaining poaching liquid to a glaze, about 7-8 minutes. Pour over pears. Refrigerate until ready to serve.
To serve, place 1/2 pear on each dish and top with a dollop of yogurt over each.