For the cheesecake: Position a rack in the middle of the oven and preheat to 325 degrees F. Brush an 8-inch springform pan with a light coating of canola oil.
Puree the mango and passion fruit juice in a food processor until smooth. Add the cream cheese and continue to process until smooth. Then add the sugar, yogurt, and cornstarch, pulsing to combine. Then add the eggs, lime zest and juice and pulse to combine. Take care not to overmix the batter. Pour batter into the prepared pan.
Bake the cheesecake until the outside of the cake is set but the center is still a little loose, about 45 minutes. Turn the oven off and open the door to let out some heat. Close door and continue to cook the cheesecake in the residual heat in the oven for 20 minutes. This gentle finish minimizes the risk of the dreaded crack in your cheesecake.
Run a knife around the edges and cool to room temperature, about 1 hour. Cover and refrigerate for 1 hour.
Meanwhile make the topping: Put about half of the passion fruit juice and all the lime juice in a medium bowl and sprinkle the gelatin over the surface. Don't stir. Set aside until the gelatin "blooms", about 1 minute. Boil the remaining passion fruit juice and all of the sugar in a small saucepan until the sugar dissolves. Whisk the hot juice into the gelatin mixture until smooth. Refrigerate until just begins to set, about 20 minutes. Stir in the fresh passion fruit pulp and seeds and pour over the top of the cooled cheesecake. Refrigerate for at least 8 hours or overnight.
To make mango coulis: Puree the passion fruit juice, mango, lime juice, and sugar in a food processor.
Bring cheesecake to room temperature 30 minutes before serving. Remove the springform ring. To serve, dip a knife in warm water, wipe dry before slicing each piece. Serve with mango coulis.
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