Combine the sugar, cream cheese, ricotta cheese, yogurt, lemon juice, flour and vanilla in the bowl of a food processor. Puree, scraping down the sides of the bowl once or twice until the mixture is completely smooth.
Pour in the egg whites and eggs and puree until smooth. Pour the mixture into the cooled, crust-lined pan.
Cover and cook over low heat for about 1 hour and 15 minutes until the center is just barely set when the pan is gently shaken.
Remove the pan from the heat and let the cheesecake stand covered for 15 to 20 minutes.
Refrigerate uncovered for at least 2 hours until the cake is completely cold and firm. Slice in to wedges and serve.