Preheat oven to 350 degrees F. Using a melon baller, core apples, leaving the bottoms intact. Using a small sharp knife, cut off a strip of peel around the top of each apple. Place apples in a 2-quart casserole or baking dish.
In a small saucepan combine apple juice, maple syrup, and butter. Bring to boiling. Pour hot juice mixture over apples. Insert a piece of stick cinnamon in the center of each apple.
Bake, uncovered, for 40 to 45 minutes or until apples are tender, brushing tops of apples occasionally with juice mixture in casserole. To serve, remove stick cinnamon. Spoon juice mixture over baked apples.