Preheat oven to 325°F.
Press the crust into an 8-inch cake or springform pan (you can use a 9-inch, but it will not be as tall) lined with parchment paper. I put the crust up the sides of my 8-inch pan, but if you want clean sides, you will have a thicker bottom crust or you can leave a portion of the crust out. It perfectly fits the bottom of a 9-inch pan, without going up the sides. Bake until golden and smells toasty.
Mix the cheesecake batter as directed in this recipe. Pour 1/4 of the cheesecake batter into the prepared pan. Shake the pan to spread the batter evenly. Create a spiral of the pomegranate juice over the batter and use a skewer to create swirls. Repeat this pattern 3 more times with the remaining batter and pomegranate juice (save a bit of pomegranate juice to decorate the top of the cheesecake).
Bake as instructed in the recipe*. (If you are using an 8-inch pan, you'll want to reduce the temperature to 300°F and bake for about 30 minutes longer, since the cake is taller. Reducing the temperature will prevent the top from getting overly brown, so the design is still visible. Low and slow baking will also prevent cracking.*If baking in a springform pan, be sure to wrap the bottom in foil to prevent the water bath from getting into the pan. Once the cake is set in the middle, run a knife around the edge of the pan, to prevent it from cracking as it cools. Allow the cake to cool in the hot water bath. Once it is room temperature, cover and refrigerate for several hours or overnight. Invert the cake onto a serving platter.